Hyperspectral image classification (HSIC) has received considerable interest in recent years where most techniques are developed to classify images with background (BKG) removed by ground truth (GT). Unfortunately, in real scenarios, obtaining complete BKG knowledge is generally infeasible. Accordingly, HSIC performed with no BKG (HSIC-NB) is not realistic. Most importantly, many techniques claim to work well for HSIC-NB but perform poorly with BKG included. This article investigates issues arising from BKG in HSIC and further presents a new approach to HSIC with BKG (HSIC-B), called one class detection (OCD), which is based on the well-known hyperspectral subpixel detection technique, constrained energy minimization (CEM). In order for OCD to perform multiclass classification, OCD is further extended to hierarchical OCD (HOC) which is particularly designed to classify multiple classes in a hierarchical tree where each layer uses an iterative kernel CEM (IKCEM) or an iterative kernel target-constrained interference-minimized filter (IKTCIMF) to detect one class at a time for classification. Since M classes are classified by OCD in${M} -1$layers in a hierarchical tree, a new concept of class classification priority (CCP) derived from CEM is specifically designed to rank all the classes along the tree in a prioritized order according to their CCP scores. The experimental results demonstrate that hierarchical OCD (HOCD) works well and performs significantly better than many existing HSIC-NB methods at the expense of slightly reduced classification accuracy compared to HSIC-N methods.

Fusarium wilt is a threatening plant infection for Phalaenopsis plants. The disease presents with symptoms such as yellowing and wilting of leaves, leading to death and possible spread to neighboring healthy plants. This study explores the use of hyperspectral imaging techniques and deep learning models to develop a non-destructive and efficient method for fusarium wilt detection. To exploit potential correlations and patterns within spectral bands, we use a 2D-CNN model as the model backbone. Finally, the integration of hyperspectral image data collection and detection models enables automated and simplified execution, providing a practical system for detecting and managing wilt in Phalaenopsis plants without manual intervention. This integration enables efficient processing of collected hyperspectral imagery, feeding it into detection models and producing reliable results.

Hepatocyte nucleus segmentation in histopathology images is vital for diagnostics. However, varying slide background due to cutting and staining poses a great challenge for domain-agnostic segmentation, which limits model generalization. This paper first proposes an anti-background perturbation consistency (APC) loss to mitigate the influence of image background on model decisions and controlled background perturbations to enhance generalizability, while still maintaining feature consistency. Since convolutional neural networks (CNNs) often prioritize local texture over global shape which also limits generalization, we then introduce the concept of local self-information into the texture probability (TP) loss to reduce over-focus of CNN on local textures. To avoid model convergence to saddle points during training which yields varying outcomes and unstable performance, we finally conclude with a meta-learner which combines results from multiple models to improve stability and better decision-making. At the end, our developed APC coupled with the texture reduction ensemble model (TREM) effectively increases model generalizability across diverse data without fine-tuning model parameters. The code of this study are available at https://github.com/s07362022/ATE.

Target detection is a fundamental task of hyperspectral imaging where constrained energy minimization (CEM) has been widely used for subpixel target detection techniques. Due to its effectiveness, CEM has been generalized to various versions, such as kernel CEM (KCEM), kernel target-constrained interference-minimized filter (KTCIMF), ensemble cascaded CEM (ECEM), and hierarchical CEM (HCEM). Unfortunately, these generalizations overlooked the key design rationale behind CEM. This article revisits CEM for hyperspectral target detection (HTD) and proves how and why it works mathematically. Specifically, several new CEM generalizations are derived and particularly noteworthy. By including spatial information in an iterative process, KCEM, ECEM, and HCEM can be generalized to iterative KCEM (IKCEM), iterative KTCIMF (IKTCIMF), iterative ECEM (IECEM), and iterative HCEM (IHCEM). Also, by utilizing an iterative random training sampling (IRTS) to generate the desired target signature to be detected, these algorithms are further generalized to IRTS KCEM (IRTS-KCEM), IRTS ECEM (IRTS-ECEM), and IRTS HCEM (IRTS-HCEM). A comprehensive analysis along with comparative study on these generalizations is conducted through extensive experiments to demonstrate the effectiveness of IKCEM, IHCEM, and IECEM.

This article investigates four issues, background (BKG) suppression (BS), anomaly detectability, noise effect, and interband correlation reduction (IBCR), which have significant impacts on its performance. Despite that a recently developed effective anomaly space (EAS) was designed to use data sphering (DS) to remove the second-order data statistics characterized by BKG, enhance anomaly detectability, and reduce noise effect, it does not address the IBCR issue. To cope with this issue, this article introduces band sampling (BSam) into EAS to reduce IBCR and further suppress BKG more effectively. By implementing EAS in conjunction with BSam (EAS-BSam), these four issues can be resolved altogether for any arbitrary anomaly detector. It first modifies iterative spectral–spatial hyperspectral anomaly detection (ISSHAD) to develop a new variant of ISSHAD, called iterative spectral–spatial maximal map (ISSMax), and then generalizes ISSMax to EAS-ISSMax, which further enhances anomaly detectability and noise removal. Finally, EAS-BSam is implemented to reduce IBCR. As a result, combining EAS, BSam, and ISSMax yields four versions: EAS-BSam, EAS-ISSMax, BSam-SSMAX, and EAS-BSam-SSMax. Such integration presents a great challenge because all these four versions are derived from different aspects, iterative spectral–spatial feedback process, compressive sensing, and low-rank and sparse matrix decomposition. Experiments demonstrate that EAS-BSam and EAS-BSam-SSMax show their superiority to ISSHAD and many current existing hyperspectral anomaly detection (HAD) methods.

Gaussian pyramid (GP) is a commonly used image coding technique which encodes an image as a pyramid which is stacked by a set of images with Gaussian window-reduced sizes and multiple spatial resolutions. Associated with GP a Laplacian pyramid (LP) can be also constructed to represent differential images between images in two consecutive layers of GP. Such resulting Gaussian-Laplacian pyramid (GLP) performs data compression in a lossless and lossy manner. A convolutional neural network (CNN) consists of a series of layers concatenated in a feedforward manner where each layer has a convolutional sublayer (CL) and a pooling sublayer (PL). Interestingly, each layer implemented by CL and PL in a CNN can be realized by a single layer in GP in the sense that CL and PL can be carried out by a low-pass Gaussian filter operated as a Gaussian kernel in a single layer of GP. This paper develops a new approach to hyperspectral image classification (HSIC), called Gaussian-Laplacian pyramid network (GLPN) which uses not only GP to realize CNN, but also LP to capture differential information between two consecutive layers that CNN cannot. Furthermore, by incorporating an iterative process into GLPN we can derive an iterative GLPN (IGLPN) that can be considered as a companion of a recently developed iterative random training sampling CNN (IRTS-CNN) by replacing CNN with GLPN. Since GLPN can realize CNN in a better way, it is expected that IGLPN will perform better than IRTS-CNN and also significantly reduce computational efficiency compared to IRTS-CNN.

For scenes with complex backgrounds and weak anomalies, how to effectively distinguish anomaly targets from the background is the key to perform hyperspectral image anomaly detection (AD). Data decomposition-based methods have been widely studied due to their potential in separating background and anomaly components. However, due to its unclean background extraction and sensitivity to noise, it has an adverse effect on the detection of anomaly targets. Additionally, a large amount of spectral data can lead to an increase in computation during data decomposition. To address this issue, we propose an AD method based on a feedback band group and variation low-rank sparse model (FBGVLRS-AD). Firstly, we employ a uniform band selection strategy to partition spectral bands and perform data decomposition on the selected band group, to separate low-rank and sparse components. This decomposition on the band group can reduce computational time and mitigate the interference from spectral variability. Secondly, to preserve the integrity of abnormal target spectra during the background extraction process, theL2,1norm is employed for joint correlated total variation to extract the desired anomalous targets. Then, utilizing the detection information from the existing band groups, a feedback-driven iterative framework has been designed to consider the consistency and complementarity in AD across band groups. This framework facilitates the extraction of sparse components in subsequent band groups and reinforces the anomalous elements. Iteratively addressing these sub-problems on band groups helps prevent the loss of useful spectral information, maintaining sufficient anomaly information while reducing interference from redundant information and spectral variations. Finally, the proposed FBGVLR-AD is optimally solved by the augmented Lagrange multiplier (ALM) method. Comparison with state-of-the-art anomaly detectors on multiple data validates the competitiveness of the proposed method for AD tasks.

Real-time anomaly detection technique can efficiently and effectively leverage available data and operates in tandem with data collection, avoiding dependence on unacquired spectral data. Nonetheless, there are no restrictions or discussions regarding the scope of utilization for existing data. Overloading the analysis with excessive information, particularly encompassing dynamically changing background scenes, can introduce interference, undermining the statistical characteristics of the data and hampering anomaly detection. Studies indicate that local anomaly detection can enhance detection performance. Consequently, determining the optimal scope of the row space within the context of real-time line-by-line processing by integrating local processing and real-time technology stands pivotal in enhancing efficacy. In order to realize real-time hyperspectral local anomaly detection, based on the most widely used push-broom hyperspectral imaging sensor, this article proposes a finite Markov local real-time correlation matrix$R$anomaly detection (FMLRT-RAD) by studying the similarity of spectra in adjacent regions of the same substance and the independence of spectra in different regions in hyperspectral images. FMLRT-RAD can adaptively determine the size of the local background region, and solve the challenging task of selecting a suitable data range for local background suppression when an imaging sensor obtains a large amount of data. In addition, based on sample correlation matrix$R$anomaly detection, two different correlation matrix representations are designed for dynamically updating finite local samples. Woodbury matrix identity is used to update background suppression, and corresponding update equations with causal recursion characteristics are derived to achieve local real-time anomaly detection to further reduce time consumption and improve detection capability. The experimental results of several real-world hyperspectral image datasets show that the detector has superior detection performance compared with other advanced detectors.

Oriented to adaptive recognition of the new land-cover categories, incremental classification (IC) that aims to complete adaptive classification with continuous learning is urgent and crucial for hyperspectral image classification (HSIC). Nevertheless, deep-learning-based HSIC models adopted the learning paradigm with fixed classes yield unsatisfactory inference in the situation of IC due to the catastrophic forgetting problem. To eliminate the recognition gap and maintain the old knowledge during IC, in this paper, we propose a novel approach called the distillation-constrained prototype representation network (DCPRN) for hyperspectral image incremental classification (HSIIC). The primary goal of DCPRN is to enhance the discriminative capability for recognizing the original classes in HSIIC, while effectively integrating both the original and incremental knowledge to facilitate adaptive learning. Specifically, the proposed framework incorporates a prototype representation mechanism, which serves as a bridge for knowledge transfer and integration between the initial and incremental learning phases of HSIIC. Additionally, we present a dual knowledge distillation module in incremental learning, which integrates discriminative information at both the feature and decision level. In this way, the proposed mechanism enables flexible and dynamic adaptation to new classes and overcomes the limitations of fixed-category feature learning. Extensive experimental analysis conducted on three popular data sets validates the superiority of the proposed DCPRN method compared with other typical HSIIC approaches.

In this paper, we build a platform that can automatically and rapidly detect Fusarium wilt on Phalaenopsis. We have also developed a portable handheld multispectral imaging device (PHMID) that contains six LEDs representing six spectral bands, making it easier to use in the field. The Automatic Target Generation Process (ATGP) and the Spectral Angle Mapper (SAM) are used to obtain the desired signal on a high-spectral image. The Harsany-Farrand-Chang (HFC) method is used for band selection to estimate the number of different spectral bands. We use deep neural networks (DNNs), support vector machines (SVMs), and random forest classifiers (RFCs) for classification. The best detection accuracy of VNIR, SWIR and PHMID was 95.77%, 91.72% and 90.84%, respectively.

Due to significant inter-band correlation resulting from use of hundreds of contiguous spectral bands, band selection (BS) is one of most widely used methods to reduce data dimensionality for band redundancy removal. A challenge for BS is how to design an effective criterion which can select bands with preserving crucial spectral information, while also avoiding selecting highly correlated bands. Information theory turns out to be one of best means to address such issue in terms of information redundancy, specifically, the rate distortion function (RDF) of Shannon’s 3rdnoisy source coding (or joint source and channel coding) theorem, which has been widely used in image compression/coding. This paper presents a novel unsupervised RDF-based band subset selection (RDFBSS) for hyperspectral image classification (HSIC). To accomplish this goal, a new concept of the area under an RDF curve, ARDFsimilar to the area under a receiver operating characteristic (ROC), Azdefined in hyperspectral target detection is coined and defined as a criterion for BSS. Since BSS generally requires an exhaustive search for an optimal band subset, two iterative algorithms similar to sequential (SQ) N-FINDR and successive (SC) N-FINDR for finding endmembers, called sequential (SQ) RDFBSS and successive (SC) RDFBSS, can be derived and coupled with Ardf as a criterion to find optimal band subsets. The experimental results demonstrate that RDFBSS is indeed a very effective BS method to find best possible band subsets and also performs better than most recent BS methods.

Anomaly detection (AD) requires spectral and spatial information to differentiate anomalies from their surrounding data samples. To capture spatial information, a general approach is to utilize local windows in various forms to adapt local characteristics of the background (BKG) from which unknown anomalies can be detected. This article develops a new approach, called iterative spectral–spatial hyperspectral AD (ISSHAD), which can improve an anomaly detector in its performance via an iterative process. Its key idea is to include an iterative process that captures spectral and spatial information from AD maps (ADMaps) obtained in previous iterations and feeds these anomaly maps back to the current data cube to create a new data cube for the next iteration. To terminate the iterative process, a Tanimoto index (TI)-based automatic stopping rule is particularly designed. Three types of spectral and spatial information, ADMaps, foreground map (FGMap), and spatial filtered map (SFMap), are introduced to develop seven various versions of ISSHAD. To demonstrate its full utilization in improving AD performance, a large number of extensive experiments are performed for ISSHAD along with its detailed comprehensive analysis among several most recently developed anomaly detectors, including classic, dual-window-based, low-rank representation model-based, and tensor-based AD methods for validation.

Convolution neural network (CNN) has received considerable interest in hyperspectral image classification (HSIC) lately due to its excellent spectral-spatial feature extraction capability. To improve CNN, many approaches have been directed to exploring the infrastructure of its network by introducing different paradigms. This paper takes a rather different approach by developing an iterative CNN which extends a CNN by including a feedback system to repeatedly process the same CNN in an iterative manner. Its idea is to take advantage of a recently developed iterative training sampling spectral-spatial classification (IRTS-SSC) that allows CNN to update its spatial information of classification maps through a feedback spatial filtering system via IRTS. The resulting CNN is called iterative random training sampling CNN (IRTS-CNN) with several unique features. First, IRTS-CNN combines CNN and IRTS-SSC into one paradigm, an architecture which has never investigated in the past. Second, it implements a series of spatial filters to capture spatial information of classified data samples and further feeds this information back via an iterative process to expand the current input data cube for the next iteration. Third, it utilizes the expanded data cube to randomly re-select training samples and then to re-implement CNN iteratively. Last but not least, IRTS-CNN provides a general framework which can implement any arbitrary CNN as an initial classifier to improve its performance through an iterative process. Extensive experiments are conducted to demonstrate that IRTS-CNN indeed significantly improves CNN, specifically, when only a small size of limited training samples is used.

Unsupervised domain adaptation (UDA) attempts to boost the performance on an unlabeled target domain by transferring knowledge from a labeled source domain. The previous models consider domain-level discrepancy while neglecting content-level distinction. To further decrease the distribution gap between different domains, this letter proposes a novel UDA approach with content-wise alignment for hyperspectral image classification (HSIC). We accomplish feature alignment with content-wise discrepancy reduction through an adversarial framework for the first time. Expressly, the core of the proposed content-wise scheme is integrated with a class-level and style-perceive-level regularized alignment to strengthen the representation of invariant feature. The experimental analysis demonstrates that the proposed model achieves more effective performance than other domain adaptation methods for hyperspectral image (HSI).

Band selection (BS) aims to choose a salient subset implied sufficient information from the numerous bands, which supplies a significantly efficient way to alleviate the barrier of dimensionality disaster for hyperspectral image classification (HSIC). This letter develops a semisupervised BS approach based on dual-constrained low-rank representation BS (DCLRR-BS) with two regularizations for HSIC. To be specific, a low-rank representation model is first proposed with super-pixel and imbalanced class-wise constraints, which are explicitly integrated to improve the performance of the band description. Next, the clusters are built adaptively based on graph theory in an unsupervised manner to rapid selection efficiency. A selection criterion is last designed to highlight the prominent band of each subset cluster to fulfill the BS procedure. Experimental results conducted on four types of classifiers with two real hyperspectral image (HSI) data sets demonstrate that the proposed DCLRR-BS method performs well in the imbalanced HSIC area.

Hyperspectral target detection (HTD) can be generally categorized by its targets to be detected,$a$prioritargets with provided known target knowledge as$a$prioritarget detection and$a$posterioritargets with known target signatures (spectral shapes), but unknown abundance fractions needed to be estimated as$a$posterioritarget detection. As a result, target detection can be performed in three scenarios, full pure-pixel target detection corresponding to$a$prioritarget detection, and subpixel and mixed-pixel target detection corresponding to$a$posterioritarget detection. To develop theories for these three types of target detection, this article develops three approaches. One is to rederive hypothesis testing-based detection theory using very basic statistical detection theory. Another two are new theories, signal-to-noise ratio (SNR)-based detection theory that uses SNR as a criterion to derive optimal detectors and spectral angle (SA)-based detection theory that calculates SA to perform HTD, both of which do not require prior probability distributions as hypothesis testing does. Specifically, it will be shown that many current hypothesis testing-derived likelihood ratio test (LRT)-based detectors can find their counterparts in the SNR-derived theory and the SA-derived detection theory. Finally, to evaluate the detection performance among the detectors developed from these three approaches, several effective detection measures resulting from 3-D receiver operating characteristic (ROC) analysis are used to conduct a comprehensive study and comparative analysis.

Hyperspectral target detection (HTD) and hyperspectral anomaly detection (HAD) are designed by completely different functionalities in terms of how to carry out target detection. Specifically, HTD is a reconnaissance technique looking for known targets as opposed to HAD which is a surveillance technique seeking unknown targets of interest. So, HTD is generally designed by the hypothesis testing theory to derive likelihood ratio test (LRT)-based detectors. However, such hypothesis testing theory-based HTD requires the targets under the alternative hypothesis to be known. In addition, it also requires knowledge of the probability distribution under each hypothesis such as Gaussian distributions. Accordingly, the LRT-based HTD cannot be directly applied to HAD. This article develops a dual theory of LRT-based HTD for HAD, which converts HTD to HAD by making LRT-based detectors anomaly detectors. In addition, by virtue of this dual theory a new signal-to-noise ratio (SNR)-based theory can be also developed for HAD. Interestingly, the commonly used hyperspectral anomaly detector, referred to as Reed and Xiaoli detector (RXD), which is derived from the generalized LRT (GLRT), can be also rederived by this dual theory as well as the new developed SNR-based HAD theory.

Band sampling (BSam) is an innovative concept for hyperspectral imaging, which is derived from signal sampling in communications/signal processing as well as sampling theory in information theory. It is quite different from band selection (BSel) in several aspects. First of all, BSam “samples” bands with a given fixed BSam rate (BSamR) as opposed to BSel, which “selects” appropriate bands according to the number of bands to be selected. Second, BSam requires no specific means of sampling bands compared to BSel, which requires a specific rule to select bands such as band prioritization (BP) criteria or band search strategies. Third, BSam samples bands without prior band knowledge or specific applications in contrast to BSel, which considers certain bands more significant than other bands according to various applications. Two strategies are developed for BSam. One is from information theory. Under a completely blind and unknown environment, the maximum entropy is achieved by the uniform distribution. This suggests that one best strategy for BSam is uniform band sampling (UBSam). Another strategy is random BSam (RBSam) analogous to random signal sampling in compressive sensing (CS) where the bands sampled by RBSam are random but are not deterministic like the bands selected by BSel. Interestingly, UBSam and RBSam generally perform better than custom-designed BSel methods. To illustrate its potential utility of BSam in various applications, target detection, anomaly detection, and image classification are studied through extensive experiments for demonstration.

CEM has shown great success in subpixel target detection. This article develops a DVT to extend CEM to CEM-AD and shows that CEM-AD also enjoys the same success in anomaly detection (AD). Its idea converts a known specific target signature$d$imposed on CEM into an unknown specific target signature to develop an SBR-CEM as a UST-CEM which serves as a liaison to derive the desired CEM-AD without prior knowledge of$d$. Surprisingly, the derived CEM-AD turns out to be a sample correlation matrix$R$-based AD,$R$-AD in correspondence to the well-known sample covariance matrix$K$-based AD developed by Reed-Xiaoli, RX-AD. To further improve CEM-AD, an LRaSMD model introduced by GoDec and its SC are further incorporated into CEM-AD where two new versions of SC, FSC and VSC, are particularly designed to enhance AD. Finally, to effectively evaluate AD performance, recently developed 3-D ROC curve-derived detection measures are used for comparative studies and analyses.

Due to unavailability of prior knowledge about anomalies, background suppression (BS) is a crucial factor in anomaly detection (AD). The difficulty with dealing with BS arises from the fact that anomalies are generally sandwiched between background (BKG) and noise. This paper presents a new concept, called effective anomaly space (EAS) to resolve this dilemma. To accomplish this goal, the well-known independent component analysis (ICA) is used to address the between BKG and anomalies issue by removing the first two orders of data statistics (2OS), while sparsity cardinality (SC) is used to address the between anomalies and noise issue by removing non-Gaussian noises and interferers from anomalies. Specifically, SC is re-derived as fixed SC (FSC) for a spectral vector and a spatial band corresponding to fixed length coding and variable SC (VSC) for a spectral-spatial sample and spatial-spectral band corresponding to variable length coding from information theory. Combining ICA and the new versions of SC allows EAS not only to remove BKG-characterized by 2OS including Gaussian-distributed signal sources, but also to remove non-Gaussian noises/interferers from anomalies. As a result, EAS can significantly increase anomaly detectability. In particular, one of great benefits resulting from EAS is that EAS can also improve current low rank and sparse representation (LRaSR)-based methods used for AD.

A known target detection assumes that the target to be detected is provideda priori, while an anomaly detection is an unknown target detection without any prior knowledge. As a result, the known target detection generally performs search-before-detect detection in an active mode, referred to as active target detection as opposed to anomaly detection which performs throw-before-detect detection in a passive mode, referred to as passive target detection. Accordingly, techniques designed for these two types of detection are completely different. This paper shows that there is indeed a mechanism, called target-to-anomaly conversion which can convert hyperspectral target detection (HTD) to hyperspectral anomaly detection (HAD) via a novel idea, called dummy variable trick (DVT). By virtue of such target-to-anomaly conversion many well-known target detection techniques, such as likelihood ratio test (LRT), constrained energy minimization (CEM) and orthogonal subspace projection (OSP), spectral angle mapper (SAM) and adaptive cosine estimator (ACE) can be converted to their corresponding anomaly detector, referred to as target-to-anomaly conversion-derived anomaly detector (TAC-AD). Since a target detector requires target knowledge while TAC-AD does not, a direct use of RAC-AD is not effective. To make TAC-AD work, a newly developed approach to effective anomaly space (EAS) is implemented in conjunction with TAC-AD so that anomalies can be retained in EAS and interference and noise including background (BKG) can be removed from EAS. The experiments demonstrate that TAC-AD operating in EAS performs better than many existing anomaly detection approaches including model-based methods.

The receiver operating characteristic (ROC) curve of detection probability (PD) versus the false alarm probability (PF), referred to as 2D ROC curve, has been widely used to evaluate hyperspectral anomaly detection (AD) performance. This article explores several fundamental and conceptual issues of a 2D ROC curve used for AD, which has been overlooked and never investigated in the past. How can a Neyman–Pearson (NP) detector work for AD? How is an ROC curve plotted without probability distributions? Why is a 2D ROC curve reported in the literature as a step function and later linearly interpolated as a linear piecewise function? How can an ROC curve be used to evaluate background suppression (BS)? To address all these issues, a mathematical theory of 2D ROC curve is rederived by a random Neyman–Pearson detector (RNPD) via a threshold parameter$\tau $, which actually determines PD and PF, and its detailed theoretical proofs along with comprehensive analysis are also provided. Specifically, a binary communication channel example is included to illustrate how RNPD works. This threshold$\tau $-driven approach, indeed, paves a way for deriving a 3D ROC curve as a function of three parameters:$\tau $, PD, and PF. By virtue of a 3D ROC curve, three 2D ROC curves of (PD,PF), (PD,$\tau$), and (PF,$\tau$) can be derived to perform AD performance analysis effectively in terms of anomaly detectability and BS. Experiments demonstrate that many anomaly detectors that claim to perform well on AD using 2D ROC curves are actually performed very poorly in BS.

Many approaches have been developed for hyperspectral anomaly detection (AD). Of particular interest are low rank and sparse representation (LRaSR) model-based methods which decompose a data space into low rank and sparse spaces. This article develops a rather different approach, which assumes that background (BKG) and anomalies can be, respectively, characterized by data statistics of the first two orders (2OS) and high orders (HOS) greater than 2. As a result, data sphering (DS) can remove BKG, while the fast independent component analysis (FastICA) can generate independent components (ICs) to form a sparse space. However, since non-Gaussian noises cannot be separated by FastICA, directly extracting anomalies from the ICs-formed sparse space may not be effective. To address this issue, a new concept of sparsity density peak (SDP) is proposed to represent the data samples in the sparse space as a probability density function from which a set of data samples with peaks can be extracted to form an anomaly space. Three versions of SDP, fixed spectral SDP (FS-SDP), fixed band SDP (FB-SDP), and spectral–spatial–sparsity peak (SS-SDP) are derived and used where the number of peaks to be extracted is determined by virtual dimensionality (VD) and a minimax-singular value decomposition (MX-SVD) algorithm. The experimental results demonstrate that DS coupled with SDP performs better than currently being used LRaSR model-based methods in AD.

Constrained energy minimization (CEM) has been extended to several generalized versions, iterative CEM (ICEM), Nystrom method-based kernel CEM (NKCEM), and iterative training sampling-based NKCEM (ITS-NKCEM) for hyperspectral image classification (HSIC). Since CEM is a subpixel target detector that specifies a target signature to detect its target abundance fractions present in data samples, this article takes the advantage of CEM’s ability in subpixel detection to consider NKCEM as a nonlinear mixed pixel classifier for hyperspectral mixed pixel classification (HMPC). Recently, a new concept of band sampling (BSam) was proposed by utilizing random signal sampling derived from compressive sensing (CS) to show its performance better than band selection (BSel) for HSIC. Thus, incorporating BSam into NKCEM and ITS-NKCEM yields two new versions for HPMC, called band sampling NKCEM (BSam-NKCEM) and band sampling ITS-NKCEM (BSam-ITS-NKCEM). Interestingly, despite that BSam-ITS-NKCEM uses sampled bands as well as training samples, extensive experiments demonstrate that it can perform better than all other CEM and KCEM versions using full bands and ground truth. Specifically, it also shows that BSam-ITS-NKCEM can do better than spectral–spatial HSIC techniques using BSel.

The target-constrained interference-minimized filter (TCIMF) has been widely used in various target detection applications for hyperspectral data exploitation. However, like other classic target detection algorithms, the complex background (BKG) of a scene significantly impacts its performance. To better cope with BKG, this article develops a BKG-annihilated TCIMF (BA-TCIMF) that can be implemented in two stages with BKG annihilation in the first stage followed by target detectability (TD) enhancement and target BKG suppression performed by TCIMF in the second stage. In particular, the second stage extracts additional BKG signatures from the BA data as unwanted signatures to enhance TD via orthogonal subspace projection (OSP) while suppressing target BKG in the BA data by constrained energy minimization (CEM). Depending upon how these two stages are carried out, three versions of BA-TCIMF, data sphered BA-TCIMF (DS-BA-TCIMF), low-rank and sparse matrix decomposition (LRaSMD) BA-TCIMF (LRaSMD-BA-TCIMF), and component decomposition analysis-BA-TCIMF (CDA-BA-TCIMF), are derived. Experimental results demonstrate that BA-TCIMF performs as it is designed and better than many existing target detection algorithms.

Low-rank and sparse representation (LRaSR)-based approaches have been widely used for anomaly detection (AD). Their central ideas are to minimize the rank of the low-rank space constrained to predetermined values, while using various regularization parameters to control the sparse representation. Three key issues arise from LRaSR. The first is how to determine the constrained rank. The second is an appropriate selection of regularization parameters. The third one is the detector used for AD. This article presents a new but rather simple competing model, called component decomposition analysis (CDA) which represents a data space X as a linear orthogonal decomposition of three components, X = PC$^{{m}} +$IC$^{{j}} +$N with${m}$principal components, PC$^{{m}}$, generated by principal component analysis (PCA) and${j}$independent components, IC$^{{j}}$, generated by independent component analysis (ICA) plus a noise component N. CDA offers several advantages over LRaSR. First, CDA uses well-known component analysis techniques to decompose the dataset without solving constrained optimization problems. Second, the values of${m}$and${j}$can be automatically determined by virtual dimensionality (VD) and a minimax-singular value decomposition (MX-SVD). To better extract anomalies from the IC$^{{j}}$component space, the concept of sparsity cardinality (SC) is further incorporated into CDA to derive a CDASC anomaly detector (CDASC-AD). The experimental results demonstrate that CDASC-AD is very competitive against the LRaSR-based models and performs well in hyperspectral AD.

This article presents a new approach, called progressive band subset fusion (PBSF) for hyperspectral anomaly detection. Unlike band selection (BS) which selects bands according to band prioritization or band search strategies, PBSF fuses band subsets progressively during data collection processing. It is completely opposite to BS that must be done after data are acquired and then select bands by removing spectral redundancy as post-data processing. To accomplish PBSF, two versions of PBSF are derived: PBSF of the multiple-band subset (PBSF-MBS) and PBSF of uniform BS (PBSF-UBS). In particular, the fusion process takes place in an anomaly detector from a real-time processing perspective. Three approaches are developed to realize PBSF of two-band subsets simultaneously: PBSF-band sequential (PBSF-BSQ), PBSF-RT, and PBSF-zigzag. Extensive experiments demonstrate that PBSF has advantages over BS in many ways.

One fundamental task of hyperspectral imaging is spectral unmixing. In this case, the conventional pure pixel-based hyperspectral image classification (HSIC) may not work effectively for mixed pixels. This article presents a kernel-based approach to hyperspectral mixed pixel classification (HMPC) which includes two nonlinear mixed pixel classifiers, kernel constrained energy minimization (KCEM) and kernel linearly constrained minimum variance (KLCMV) to replace the widely used pure pixel-based support vector machine (SVM) classifier. Interestingly, what the binary-class and multiclass SVM classifiers are to pure pixel-based HSIC can be similarly derived for what a single-class KCEM detector and a multiclass KLCMV detector are to HMPC. In particular, the commonly used discrete classification map-based hard classification measures, average accuracy (AA) and overall accuracy (OA) for performance evaluation can be further generalized to real-valued mixed class abundance fractional map-based soft classification measures via 3-D receiver operating characteristic (3-D ROC) analysis-derived detection measures. Extensive experiments are conducted to demonstrate the utility of HMPC where KCEM/KLCMV not only significantly improve the classification performance of CEM/LCMV-based classifiers but also outperform many existing spectral-spatial classification methods.

This article presents a multispatial filtering module cascaded system (MSFMCS) for hyperspectral image classification (HSIC), which can serve as a paradigm to improve spectral–spatial classification. It includes multiple spatial filtering modules (SFMs) that are cascaded to particularly capture spatial information from the classification maps generated from the preceding modules. As a result, any spectral classifier (SC) can be used as an input to an initial/input module (IM). Through MSFMCS, its classification performance keeps improving as more SFMs are processed. To terminate MSFMCS, an automatic stopping rule is particularly designed by support vector machine (SVM) which is used not only as a classifier but also as a decision-maker. So, once an SC cannot be further improved, MSFMCS is terminated. One major benefit resulting from MSFMCS is its framework which can implement any arbitrary SC as its initial classifier in IM. Another is its ability in capturing additional spatial classification information module by module as the process progresses. A third one is no weights connected between modules so that no training phase is required like a feedforward neural network. Finally, the number of modules used in MSFMCS can be automatically determined by its stopping rule not predetermined empirically. To illustrate full advantages of MSFMCS in HSIC, three types of heterogeneous classifiers, pure-pixel-based SVM, mixed-pixel-based constrained energy minimization (CEM), and feature-extraction-based classifier—orthogonal total variation component analysis (OTVCA)—are used for experiments to demonstrate how MSFMCS can improve their classification performance.

This article proposes a new approach to hyperspectral band processing for anomaly detection, to be called sequential band fusion (SBF), derived from the band sequential (BSQ) data acquisition format used by a hyperspectral imaging sensor which fuses one single band at a time with previously fused band subset sequentially. In order to realize SBF, four versions, SBF-BSQ, initial band driven SBF (IBD-SBF), band prioritization SBF (BP-SBF), and band selection SBF (BS-SBF), are developed. Furthermore, to validate the sequentially fused results by SBF identical to that produced by combining all joint bands together, its mathematical theory and derivations are also presented. Finally, the full utility of SBF in anomaly detection is demonstrated through extensive experiments.

This article presents a bi-endmember semi-nonnegative matrix factorization (Semi-NMF) algorithm based on low-rank and sparse matrix decomposition (LRSMD), referred to as BLSNMF, to resolve the issues of endmember variability and nonlinear mixing. Given the fact that the hyperspectral images contain a large amount of redundant information, compressing sensing (CS) techniques can generally be used to randomly sense the effective information in an observed image according to the effective approximation of the bi-endmember components. In this article, the proposed BLSNMF integrates low-rank and sparse spaces decomposed by go decomposition (GoDec) or orthogonal subspace projection-based go decomposition (OSP-GoDec) with Semi-NMF to suppress interference between different components so as to improve the unmixing performance via a simple linear mixed model. Specifically, the observed data space is first decomposed by GoDec or OSP-GoDec to approximate four different attribute components, CS-sampled double low-rank components, structured sparse component, and noise component. Second, from the CS-sampled double low-rank components, the inherent and new endmembers along with their abundances are evaluated via Semi-NMF, and then, the double low-rank components are redescribed using the estimated endmembers and abundances. Finally, the serious interference entries in the structured sparse component space are removed from the data to better learn other attribute components. The experimental results show that BLSNMF can eliminate the interference of new endmembers and sparse noise so as to better evaluate the endmembers and abundances and effectively improve the ability to interpret the spectral information.

Despite continuing to progress in hyperspectral image classification (HSIC) based on deep learning, the classification accuracy is limited to furtherly improve in the absence of labeled samples. To address this issue, the metric-based prototypical networks for few-shot learning have enjoyed widespread popularity. However, the conventional prototypical networks are vulnerable to the selected examples and fail to accomplish representative predictions for the prototypes in complicated situations. In this paper, we propose a multi-view calibrated prototype-learning framework for few-shot HSIC, which consists of three rectified strategies from different views to improve the robustness of prototypes in the embedding space. Specifically, the calibrated aggregation network is the first presented to calibrate the representations with local patches aggregation for the enhancement of the prototypes. Moreover, to improve the compactness of the intraclass expression, the calibrated metric learning with regularization terms is designed to strengthen the discrimination of the prototypes. Furthermore, we calibrate the feature distribution of supervised samples by transferring statistical knowledge to eliminate the local bias in the test phase. The extensive experimental results and analysis of three hyperspectral image datasets demonstrate the superiority of the proposed architecture compared with other advanced methods.

Hyperspectral image classification (HSIC) methods based on convolutional neural network (CNN) continue to progress in recent years. However, high complexity, information redundancy, and inefficient description still are the main barriers to the current HSIC networks. To address the mentioned problems, we present a spatial-spectral dense CNN framework with a feedback attention mechanism called FADCNN for HSIC in this article. The proposed architecture assembles the spectral-spatial feature in a compact connection style to extract sufficient information independently with two separate dense CNN networks. Specifically, the feedback attention modules are developed for the first time to enhance the attention map with the semantic knowledge from the high-level layer of the dense model, and we strengthen the spatial attention module by considering multiscale spatial information. To further improve the computation efficiency and the discrimination of the feature representation, the band attention module is designed to emphasize the weight of the bands that participated in the classification training. Besides, the spatial-spectral features are integrated and mined intensely for better refinement in the feature mining network. The extensive experimental results on real hyperspectral images (HSI) demonstrate that the proposed FADCNN architecture has significant advantages compared with other state-of-the-art methods.

The current hyperspectral image classification (HSIC) model based on the convolutional neural network for feature extraction and softmax classifier has been prone to the barrier of label prediction with limited samples. Substituting for the enormously complicated work of terrain labeling, few-shot learning provides a popular option for HSIC with very few annotated samples. In this paper, we proposed a novel edge-inferring framework with the meta-learning paradigm for hyperspectral few-shot classification (HSFSC). In which, a graph neural network for similarity measurement is firstly presented to iteratively infer edge labels with the exploitation of instance-level similarity and the distribution-level similarity. Besides, in the meta-training stage, the pixel prediction model and patch prediction model based on edge inferring architecture are concretized jointly to improve the classification accuracy of the test samples. Expressly, at the meta-testing phase, the dynamic task-guided self-diagnosis strategy is developed for the first time to diagnose the samples separability of the current classification task, which is responsible for dynamically assigning the most reliable results based on the generated reliability grade of the sample. The extensive experimental results and analysis of three hyperspectral image datasets demonstrate the superiority of the proposed HSFSC architecture compared with other advanced methods.

Hyperspectral image (HSI) provided with a substantial number of correlated bands causes calculation consumption and an undesirable "dimension disaster" problem for the classification. Band selection (BS) is an effective measure to reduce the information redundancy with the physics spectrum preserved for HSI. Although the existing BS methods have achieved noticeable progress, the correlation between neighbor bands still needs to be mined deeply for an effective selection criterion. This paper proposes a BS approach to collecting the discriminative band subset for hyperspectral image classification (HSIC), which adopts the self-supervised learning paradigm to implement the BS by auxiliary spectrum rebuilding task. In specific, we utilized a Convolutional neural network (CNN) and Graph Convolutional Network (GCN) for the spectral-spatial feature extraction. Next, GCN and CNN are developed for the refinement of the band correlation sequentially. Afterward, the selected bands in terms of the acquired correlation are fed into the presented self-supervised spectrum rebuilding network for spectral reconstruction. Simultaneously, the proposed architecture completed the selection with the optimization of the band reconstruction by a defined loss function. In this way, we supply substitution for selection criterion and path searching through the end-to-end framework. The extensive experimental results and analysis demonstrated that the proposed hybrid architecture provided a competitive band subset for the classification, and the accuracies with different types of classifiers are more effective than the compared BS methods.

In this paper, we combined hyperspectral imaging techniques and deep neural networks (DNN) to detect Fusarium wilt on Phalaenopsis. Spectral angle mapper (SAM) and constrained energy minimization (CEM) were used to find abnormal areas. Band selection (BS) methods include Harsanyi-Farrand-Chang (HFC), band priority (BP) and band decorrelation (BD) were applied to get effective bands. The results showed that, on the fifth day of Phalaenopsis infection, the best accuracy rates for detecting Fusarium wilt using VNIR and SWIR hyperspectral imaging were 93.5% and 94.9%, respectively. In most cases, the accuracy of using DNN is better than using support vector machine (SVM).

Iterative constrained energy minimization (ICEM) has shown success in classification. However, a drawback suffered from ICEM is its requirement of complete ground truth to calculate class means. This letter develops an iterative selection of training samples to extend ICEM with two versions: iterative fixed training sampling constrained energy minimization (CEM) (IFTS-CEM) which uses a fixed training sample set throughout the entire iterative process and iterative random training sampling CEM (IRTS-CEM) which uses a random training sampling (RTS) at each iteration. The experimental results demonstrate that IRTS-CEM performs better than IFTS-CEM and also comparable to ICEM.

Receiver operating characteristic (ROC) analysis is performed by a curve, called ROC curve, plotted based on detection probability, PD, versus false alarm probability, PF, and has been widely used as an evaluation tool for signal detection. Specifically, the area under an ROC curve (AUC) is calculated and used as a detection measure. Unfortunately, finding distributions of PDand PFto generate a continuous ROC curve is practically infeasible. This article investigates approaches to generating a discrete 2D ROC curve of ( PD, PF) without appealing for probability distributions. Since PDand PFare determined by the same threshold τ to specify a detector, an ROC curve of ( PD, PF) can only be used to evaluate the effectiveness of a detector but not target detectability (TD) and also not background suppressibility (BS). To address this issue, a 3D ROC curve is generated as a function of ( PD, PF, τ) by introducing a specific threshold parameter τ as a third independent variable. As a result, a 3D ROC curve along with its derived three 2D ROC curves of ( PD, PF), ( PD, τ), and ( PF, τ) can further be used to design new quantitative measures to evaluate the effectiveness of a detector and its TD and BS. To demonstrate the full utility of 3D ROC analysis in target detection, extensive experiments are performed on two types of targets, prior target detection and anomaly detection, to conduct a comprehensive analysis on 3D ROC curves using new designed detection measures to evaluate target/anomaly detection performance.

Orthogonal subspace projection (OSP) has been widely used in many applications for hyperspectral data exploitation. However, its performance is sensitive to its used prior target knowledge, which is significantly affected by target background (BKG). To resolve this issue, this article develops three approaches to extend OSP in improving its performance. One is data sphering which can suppress BKG via removing the first- and second-order data statistics. Another takes advantage of a recently developed low-rank and sparse matrix decomposition (LRaSMD) to separate BKG and target signal sources in two subspaces characterized by the low-rank matrix and sparse matrix, respectively, and then annihilates BKG via the low-rank matrix, referred to as BKG-annihilated OSP (BA-OSP). A third approach combines data sphering and LRaSMD to further improve OSP over target detectability and BKG suppressibility. Experiments show that implementing OSP in conjunction with data sphering and LRaSMD significantly improves OSP in target detection and BKG suppression, and also performs as well as a widely used constrained energy minimization (CEM)-based subpixel target detection.

Low-rank and sparsity-matrix decomposition (LRaSMD) has received considerable interests lately. One of effective methods for LRaSMD is called go decomposition (GoDec), which finds low-rank and sparse matrices iteratively subject to the predetermined low-rank matrix order m and sparsity cardinality k. This article presents an orthogonal subspace-projection (OSP) version of GoDec to be called OSPGoDec, which implements GoDec in an iterative process by a sequence of OSPs to find desired low-rank and sparse matrices. In order to resolve the issues of empirically determining p = m + j and k, the well-known virtual dimensionality (VD) is used to estimate p in conjunction with the Kuybeda et al. developed minimax-singular value decomposition (MX-SVD) in the maximum orthogonal complement algorithm (MOCA) to estimate k. Consequently, LRaSMD can be realized by implementing OSP-GoDec using p and k determined by VD and MX-SVD, respectively. Its application to anomaly detection demonstrates that the proposed OSP-GoDec coupled with VD and MX-SVD performs very effectively and better than the commonly used LRaSMD-based anomaly detectors.

Due to significant inter-band correlation resulting from the use of hundreds of contiguous spectral bands, band selection (BS) is commonly used to reduce data dimensionality for band redundancy removal. A challenge for BS is how to design an effective criterion which can select bands with crucial self-retained spectral information, while also avoiding highly correlated bands to be selected. This article presents a novel approach, referred to as self-mutual information-based band selection (SMI-BS) for hyperspectral image classification (HSIC) to address these two issues. It first constructs a hyperspectral band channel from a hyperspectral image and then takes advantage of such a band channel to coin a new concept of SMI, which is defined as the mutual information (MI) between a selected band, b, and the set of full bands, Ω, I(b; Ω). As a result, a curve plotted as a function of I(b; Ω) versus individual band b, called SMI curve, can be used as a BS criterion which selects those bands with large I(b; Ω) values as desired bands. Since such selected bands may be highly correlated, another new concept, called prominent band (PB), which is defined as a band corresponding to a prominent peak of an SMI curve, is further introduced to avoid selecting highly inter-correlated spectral bands. To validate the utility of SMI-BS in HSIC, experiments are conducted to compare existing state-of-the-art BS methods for performance evaluation. The results demonstrate that SMI-BS is indeed a very effective BS method and also performs better than other test BS methods.

Due to significant geometric distortions and illumination differences, developing techniques for high precision and robust multisource remote sensing image registration poses a great challenge. This article presents an iterative image registration approach, called iterative scale-invariant feature transform (ISIFT) for remote sensing images, which extends the traditional scale-invariant feature transform (SIFT)-based registration system to a close-feedback SIFT system that includes a rectification feedback loop to update rectified parameters in an iterative manner. Its key idea uses consistent feature point sets obtained by maximum similarity to calculate new alignment parameters to rectify the current sensed image and the resulting rectified sensed image is then fed back to update and replace the current sensed image as a new sensed image to reimplement SIFT for next iteration. The same process is repeated iteratively until an automatic stopping rule is satisfied. To evaluate the performance of ISIFT, both the simulated and real images are used for experiments for the validation of ISIFT. In addition, several data sets are particularly designed to conduct a comparative study and analysis with existing state-of-the-art methods. Furthermore, experiments with different rotation are also performed to verify the adaptability of ISIFT under different rotation distortions. The experimental results demonstrate that ISIFT improves performance and produces better registration accuracy than traditional SIFT-based methods and existing state-of-the-art methods.

Training sample selection is a great challenge for hyperspectral image classification (HSIC), specifically when only a very limited number of labeled data samples are available for training. Two recently developed concepts for training sample selection are of particular interest. One is active learning (AL), which augments labeled training samples by including unlabeled data samples as new training samples. The other is iterative training sampling (ITS), which expands data cubes by including additional spatial classification information into the training samples. This article combines AL and ITS simultaneously to derive a joint ITS–AL spectral–spatial (SS) classification approach, to be called ITS augmentation by AL spectral–spatial classification, referred to as ITSA-AL-SS, which can improve SS classification using either AL or ITS alone. The novel idea of ITSA-AL-SS is to take advantage of ITS to expand data cubes by incorporating additional spatial classification information iteratively into the AL-augmented unlabeled data samples to update the current training samples iteration by iteration in one-shot operation. As expected, ITSA-AL-SS is benefited from both ITS and AL to not only further improve classification accuracy but also reduce classification inconsistency.

Compressive sensing (CS) has recently been demonstrated as an enabling technology for hyperspectral sensing on remote and autonomous platforms. The power, on-board storage, and computation requirements associated with the high dimensionality of hyperspectral images (HSI) are still limiting factors for many applications. A recent work has exploited the benefits of CS to perform HSI classification directly in the compressively sensed band domain (CSBD). Since the required number of compressively sensed bands (CSBs) needed to achieve full band performance varies with the complexity of an image scene, this article presents a progressive band processing (PBP) approach, called progressive CSB classification (PCSBC), to adaptively determine an appropriate number of CSBs required to achieve full band performance, while also providing immediate feedback from progressions of class classification predictions carried out by PCSBC. By taking advantage of PBP, new progression metrics and stopping criteria are also designed for PCSBC. Four real-world HSIs are used to demonstrate the utility of PCSBC.

Wealthy spectral information provided by hyperspectral image (HSI) offers great benefits for many applications in hyperspectral data exploitation. However, processing such high-dimensional data volumes that may result in redundant bands due to its high interband correlation will be a challenge. For target detection and classification, this is particularly true since there may only need a relatively small number of bands that respond one particular target of interest well, while most of other bands do not. Band selection (BS) is a major dimensionality reduction technique to remove the redundant bands and selects a few bands to represent the entire image. However, how to eliminate the effect of uninteresting targets with similar spectra on detection of interesting targets is a severe issue arising in target detection for BS. This article develops a new approach called target-constrained interference-minimized BS (TCIMBS) which can be used to select band subset for specific target detection, while annihilating targets of no interest and suppressing interferers and background. Its idea is derived from target-constrained interference-minimized filter (TCIMF). By taking advantage of TCIMF, two band prioritization (BP) criteria called forward minimum variance BP (FMinV-BP) and backward maximum variance BP (BMaxV-BP) along with their three band search-based BS counterparts called sequential forward TCIMBS (SF-TCIMBS), sequential backward TCIMBS (SB-TCIMBS), and improved SB-TCIMBS (SB-TCIMBS*) are derived. The experimental results suggest that TCIMBS can improve the detection accuracy and also achieve better performance in comparison with several state-of-the-art methods.

A spectral-spatial (SS) hyperspectral classifier generally implements a spectral classifier (SC) followed by a spatial filter (SF) for classification. This article develops a new approach to fusing multiple SC-SF classifiers for hyperspectral image classification (HSIC) as to improve classification performance. To accomplish this goal an iterative process is particularly designed to fuse the spatial-filtered classification maps (SFMaps) produced by each of SC-SF classifiers into one single SFMap via maximum a posteriori (MAP) criterion. Such fused SFMaps are then fed back and added to the current data cube to create a new data set for next round SC-SF classifier fusion. The same process is repeated iteratively until it satisfies an automatic stopping rule. To further fuse more than two SS methods, two approaches are also developed, called simultaneous multiple SC-SF fusion (SMSSF) method and progressive multiple SC-SF fusion (PMSSF) method. Experimental results demonstrate that fusing multiple SC-SF classifiers can indeed perform better than using an individual single SC-SF classifier alone without fusion.

Low rank and sparsity matrix decomposition (LRaSMD) has received considerable interest lately. One of effective methods is called go decomposition (GoDec) which finds low rank and sparse matrices iteratively subject to a predetermined low rank order, m and a sparsity cardinality, k, In order to resolve issue of the empirically determined m and k, the well-known virtual dimensionality (VD) and a minimax-singular value decomposition (MX-SVD) developed in maximum orthogonal complement algorithm (MOCA) are used for this purpose. The constrained energy minimization (CEM) is used for experiments to demonstrate that the GoDec with VD and MX-SVD performs very effectively.

Classification is a major task in hyperspectral image (HSI) processing. This paper develops an approach by taking advantage of low rank matrix derived from the low rank and sparse matrix decomposition (LRSMD) model which decomposes a hyperspectral data matrix X as X = L+S+n where L, S and n are referred to low rank, sparse and noise matrices respectively. The hyperspectral image classification (HSIC) is then performed on the low rank matrix L rather than the original data matrix X where the well-known go decomposition (GoDec) is used to produce such LRSMD model. To determine the two key parameters used in GoDec, the rank of L, m, and the cardinality of the sparse matrix, k the well-known virtual dimensionality (VD) and minimax-singular value decomposition (MX-SVD) methods are used for this purpose. Finally, to demonstrate advantages of using the low rank matrix L, support vector machine (SVM) and an edge-preserving filters (EPF)-based classifiers are implemented to evaluate classification performance.

Anomaly detection is an important application in hyperspectral data exploitation. This paper develops a novel fast low rank approximation and sparsity representation approach to anomaly detection. It first uses a standard random projection approach to construct low rank matrix, and then use it to calculate sparsity representation, S. Secondly, continuous to decompose S to get new low rank and sparsity representation until S converges into predefined threshold. Sum all S in the iteration process. Thirdly, using the summation of S to construct original matrix's low rank. Finally, comparing with state-of-art methods like Go Decomposition (GoDec), our method is seven times faster than GoDec's. The experimental on real hyperspectral images results indicate that the detection power of Reed-Xiaoli detector (RXD) is approximately increased 11% based on our sparsity representation comparing with GoDec method but the false alarm is lower than GoDec's.

In this paper, we propose a method to inspect the quality of Phalaenopsis by using hyperspectral imaging techniques. Phalaenopsis is easy to get infected with Fusarium wilt. We use the k-means clustering method to find out that the reflection spectrum of Phalaenopsis stem changes. The methods of the Spectral Angle Mapper (SAM) and Constrained Energy Minimization (CEM) are then used to find the area of the infected area. The Harsanyi, Farrand and Chang (HFC) methods and virtual dimensions (VD) are used to estimate the amount of spectrum required for band selection (BS). Band priority (BP) is used to calculate the priority of each band, and band de-correlation (BD) will remove band data with high correlation with each other. Then use the support vector machine (SVM) to detect Phalaenopsis wilt. The detection accuracy of VNIR and SWIR is 0.81 and 0.86, respectively, with band selection.

This paper develops band fusion techniques to fuse hyperspectral data from a data communication and transmission perspective. It can provide progressive profiles of fusing different bands and improve the efficiency by data processing. Anomaly detection is investigated for its application to demonstrate its utility. The experimental results prove that the proposed band fusion methods can not only ensure the accuracy of the detection results, but also can improve the data processing efficiency.

Hyperspectral imagery provides wealthy spectral information to make it suitable for many applications. However, for specific applications, extracting suitable bands from high-dimensional data is a tedious and difficult task. In the past, many methods have been developed to perform band selection for specific tasks such as target detection. However, there is very little work to consider and deal with the effects of suspected interfering targets. In this paper, a new method for band selection, called target-constrained interference-minimized band selection (TCIMBS) is developed for specific target detection. It can select a band set with strong characterization capabilities for desired targets and good suppression for undesired targets and background (BKG). Experimental results demonstrate that TCIMBS can improve the detection performance, and also achieve better performances in comparison with several state-of-the-art methods.

This letter introduces a new approach to hyperspectral image classification (HSIC), called progressive band selection processing of hyperspectral image classification (PBSP-HSIC), which performs classification in multiple stages in the sense that each stage performs HSIC progressively according to a specifically selected band subset. Interestingly, such PBSP-HSIC offers a rare view of how different classes are classified in progressive stages, which has never been explored in the past. The experimental results also show that PBSP-HSIC performs better than HSIC using full bands.

N-finder algorithm (N-FINDR) has been widely used for finding endmembers in hyperspectral imagery. Since N-FINDR must find all endmembers simultaneously, it requires exhausting all possible p-endmember combinations among the entire data samples with p being the number of endmembers required to be found. Accordingly, directly implementing N-FINDR is practically infeasible. To mitigate this dilemma, two recently developed algorithms called sequential N-FINDR (SQ N-FINDR) and successive N-FINDR (SC N-FINDR) were developed. However, even such an exhaustive search issue can be resolved numerically, another challenging issue for N-FINDR, which remains unsolved, is spectral dimensionality reduction. Because a p-vertex simplex is embedded in a (p-1)-dimensional spectral data space, N-FINDR does not require full spectral dimensionality to calculate simplex volume (SV). This article presents a compressive sensing (CS) approach to N-FINDR that can find a p-vertex simplex with the maximal SV by SQ/SC N-FINDR in a compressively sensed band domain (CSBD). In particular, to make this idea work, a new CS-based property called restricted SV property (RSVP) can be shown to be preserved in CSBD via a sensing matrix. It is this property that allows what N-FINDR and SQ/SC N-FINDR can achieve in the original data space (ODS) to be also achieved in CSBD. To further show the utility of SQ/SC N-FINDR in both ODS and CSBD as well as SV preserved by RSVP, a series of experiments are conducted for performance analysis.

The restricted isometry property (RIP) and restricted conformal property (RCP) are two fundamental properties widely used in compressive sensing (CS) for sampling sparse signals. These two properties are sufficient to preserve the magnitude of a signal vector and the angle between two signal vectors in the compressively sensed band domain (CSBD), respectively. This article derives two new CS properties for hyperspectral signal vectors (HSVs), to be called the restricted entropy property (REP) and restricted spectrum property (RSP), which can be shown to preserve the entropy of an HSV and the spectral similarity between two HSVs in CSBD in correspondence to RIP and RCP, respectively. These two properties enable hyperspectral analysis algorithms to be directly applied to CSBD without loss of data integrity, while the dimensionality of CSBD can be considerably reduced. Most importantly, REP and RSP preserve exploitation algorithm performance without the need for decompression so as to avoid specifying a sparse basis.

Recently, autoencoder (AE)-based anomaly detection has drawn considerable interest in hyperspectral image (HSI) analysis. In this article, we propose a novel discriminative reconstruction method for hyperspectral anomaly detection images with spectral learning (SLDR). The proposed algorithm has the following innovations. First, we use the spectral error map (SEM) to detect anomalies because the SEM can preferably reflect the spectral similarity of each pixel between the input and the reconstruction. Second, the loss function of the proposed SLDR model additionally introduces the spectral angle distance (SAD), which constrains the model to generate a reconstruction having greater spectral similarity to the input. Third, a constraint is imposed on the encoder, forcing it to generate latent variables that obey a unit Gaussian distribution, which helps the decoder to reconstruct a better background with respect to the input. Compared with the Reed-Xiaoli (RX), collaborative representation detection (CRD), attribute and edge-preserving filtering-based anomaly detection (AED) and adversarial autoencoder-based anomaly detection (AAE), through two real HSI data sets, the detection performance of the proposed SLDR method is found to be competitive.

Hyperspectral image classification (HSIC) faces three major challenging issues, which are generally overlooked. One is how to address the background (BKG) issue due to its unknown complexity. Another is how to deal with imbalanced classes since various classes have different levels of significance, particularly, small classes. A third one is fractional class membership assignment (FCMA) resulting from a soft-decision classifier. Unfortunately, the commonly used classification measures, overall accuracy (OA), average accuracy (AA), or kappa coefficient are generally not designed to cope with these issues. This article develops a 3-D receiver operating characteristic (3-D ROC) analysis from a detection point of view to explore how these three issues can be resolved for HSIC. Specifically, it first develops one-class classifier in BKG (OCCB), called constrained energy minimization (CEM), and multiclass classifier in BKG (MCCB), called linearly constrained minimum variance (LCMV) in conjunction with 3-D ROC analysis to address the BKG issue. Then, by considering a small class as a signal to be detected, its class accuracy can be interpreted as signal detection power/probability so that the 3-D ROC analysis can be used to address the imbalanced class issue. Finally, FCMA can be treated as a detector by converting a soft-decision classifier to a hard-decision classifier in such a manner that the 3-D ROC analysis is also readily applied. The experimental results demonstrate that 3-D ROC analysis provides a very useful evaluation tool to analyze the classification performance.

Theoretically, hyperspectral images (HSIs) are capable of providing subtle spectral differences between different materials, but in fact, it is difficult to distinguish between background and anomalies because the samples of anomalous pixels in HSIs are limited and susceptible to background and noise. To explore the discriminant features, a spectral adversarial feature learning (SAFL) architecture is specially designed for hyperspectral anomaly detection in this article. In addition to reconstruction loss, SAFL also introduces spectral constraint loss and adversarial loss in the network with batch normalization to extract the intrinsic spectral features in deep latent space. To further reduce the false alarm rate, we present an iterative optimization approach by a weighted suppression function that depends on the contribution rate of each feature to the detection. In particular, the structure tensor matrix is adopted to adaptively calculate the contribution rate of each feature. Benefiting from these improvements, the proposed method is superior to the typical and state-of-the-art methods either in detection probability or false alarm rate.

Owing to significantly improved spectral resolution, a hyperspectral imaging sensor can now uncover many unknown subtle material substances. In many cases, anomalies are usually embedded in the background. To develop a means through which these anomalies may be detected and separated from the background, we propose a spectral-spatial anomaly detection method based on a selected band subset. To be specific, we constrain an unsupervised network by making full use of the underlying physical characteristics which are beneficial to hyperspectral anomaly detection. Based on that, a selection criterion is constructed to adaptively select a subset of bands that essentially contain discriminative and informative features between the anomaly and background in an unsupervised manner. Then, the selected bands are simultaneously inputted into the spatial detector and spectral detector. To overcome the deficiencies of detecting anomalies in only one aspect, an adaptive combination of spatial result and the spectral result is introduced. Finally, a simple and powerful iterative suppression is conducted on the initial detection map to further reduce false alarm rate while ensuring detection capability. Extensive empirical researches performed on eighteen publicly available hyperspectral images (HSIs) of different sizes over different scenes demonstrate that our proposed method can achieve an average detection capability of 0.99564, and the average false alarm rate is one order of magnitude lower than the second one.

This paper presents a new band selection approach, called uniform band interval divided band selection (UBIDBS) which uniformly divides a band range into a finite number of band intervals from which a band can be selected from each band interval according to a custom designed band prioritization (BP) criterion. Two BP criteria are introduced. One is derived from orthogonal subspace projection (OSP). The other is based on correlation matrix R originated from constrained energy minimization (CEM). These two criteria allow users to identify a most significant band to be selected in each of band intervals. As a result, it avoids band decorrelation required by BP to remove adjacent high- correlated bands.

Hyperspectral image classification (HSIC) has received considerable interest in recent years. In particular, spectral-spatial classification methods are proposed to jointly consider spectral and spatial together. However, one of challenging issues in hyperspectral image classifications is the random training sample selection which produces inconsistent results. A general approach to resolving this problem is so-called k-fold method which implements randomly selected training samples k times and takes their average with respect to the standard deviation to be used describe a confidence interval. This paper develops an approach to mitigating such a random issue by introducing an iterative process to remove uncertainty caused by randomness. Its idea is to repeatedly feedback the classification results in an iterative manner that the randomness caused by the randomly selected samples can be largely reduced. The iterative process is terminated as long as the classification results obtained by two consecutive iterations agree with a prescribed tolerance. Experimental results demonstrate that our proposed method works very effectively not only to reduce result inconsistency but also to improve classification results.

Fusarium wilt on Phalaenopsis is a disease that makes farmers suffer seriously. Although Phalaenopsis does not die immediately with Fusarium wilt, it seriously decreases the quality that buyers cannot accept. In this paper, we introduce an emerging method to detect Fusarium wilt at the base of Phalaenopsis stems. The detection model divides Phalaenopsis samples into two categories, healthy and infection. The band selection (BS) processing technique based on band prioritization (BP) is applied to extract significant bands and eliminate redundant bands. Subsequently, some algorithms which are constrained energy minimization (CEM), spectral information divergence(SID) and SeQuential N-FINDER to detect the Fusarium wilt, and we hope the research would help farmers decrease their losses.

Urban impervious surface area (ISA) is a key index toward urban eco-system and sustainable urban planning strategy. In this paper, a subpixel approach is proposed to estimate urban ISA values using linear spectral mixture analysis (LSMA)-based hyperspectral imaging techniques. In doing so the concept of virtual dimensionality (VD) is used to first estimate the number of endmembers, then an endmember finding approach is implemented to find VD-determined number of endmembers in a hyperspectral image. Finally, nonnegativity constrained least squares (NCLS) is performed for endmember unmixing. The hyperspectral image used in our approach provides a larger number of spectral dimensions than a multispectral image does so that a sufficient number of endmembers can be found from a hyperspectral image for ISA estimation. What is more, a relationship between ISA values and fractional endmember abundances can be further constructed by linear regression.

Target detection (TD) is one of the major tasks in hyperspectral image (HSI) processing, and its performance is greatly affected by the background. Feature extraction (FE) has been an effective way to mine discriminative information, especially FE based on deep learning, which can learn the intrinsic properties of data to further improve the detection performance. Unlike supervised networks, unsupervised stacked sparse autoencoders (SSAEs) can learn deep and nonlinear features without any labeled data. However, SSAEs usually require a supervised fine-tuned model to obtain better discrimination, which is not feasible for TD, since the prior information is generally insufficient. In this letter, we introduce a distance constraint that is added to the SSAE to form a new distance constrained SSAE (DCSSAE) network. Specifically, the distance constraint maximizes the distinction between the target pixels and other background pixels in the feature space. Then, using the discriminative features learned from the DCSSAE, a simple detector using radial basis function kernel is derived for background suppression. Experiments on two HSIs demonstrate that the deep spectral features learned from the DCSSAE are more distinguishable, and our proposed detector, namely, the DCSSAE detector, outperforms several popular detectors, especially in background suppression.

This letter extends one of popular spectral-spatial classification methods for hyperspectral images, called edge preserving filtering (EPF)-based method to an iterative version of EPF method, referred to as iterative EPF (IEPF). Instead of finding maximum of the final soft probability maps obtained from the initial binary probability maps by EPF, the proposed IEPF feeds back the soft probability maps and combines them with the currently being processed image cube to create a new image cube as the next input to IEPF to reimplement support vector machine (SVM) for classification. The process is carried out iteratively by repeatedly feeding back the spatial information provided by EPF-obtained soft probability maps and terminated by a Tanimoto index (TI)-based automatic stopping rule. The experimental results demonstrate that IEPF performed better than EPF by providing higher classification accuracy.

This paper presents a statistical detection theory approach to hyperspectral image (HSI) classification which is quite different from many conventional approaches reported in the HSI classification literature. It translates a multi-target detection problem into a multi-class classification problem so that the well-established statistical detection theory can be readily applicable to solving classification problems. In particular, two types of classification, a priori classification and a posteriori classification, are developed in corresponding to Bayes detection and maximum a posteriori (MAP) detection, respectively, in detection theory. As a result, detection probability and false alarm probability can also be translated to classification rate and false classification rate derived from a confusion classification matrix used for classification. To evaluate the effectiveness of a posteriori classification, a new a posteriori classification measure, to be called precision rate (PR), is also introduced by MAP classification in contrast to overall accuracy (OA) that can be considered as a priori classification measure and has been used for Bayes classification. The experimental results provide evidence that a priori classifier as Bayes classifier which performs well in terms of OA does not necessarily perform well as a posteriori classifier in terms of PR. That is, PR is the only criterion that can be used as a posteriori classification measure to evaluate how well a classifier performs.

Hyperspectral anomaly detection faces various levels of difficulty due to the high dimensionality of hyperspectral images (HSIs), redundant information, noisy bands, and the limited capability of utilizing spectral-spatial information. In this paper, we address these problems and propose a novel approach, called spectral-spatial feature extraction (SSFE), which is based on two main aspects. In the spectral domain, we assume that the anomalous pixels are rarely present and all (or most) of the samples around the anomalies belong to background (BKG). Using this fact, we introduce a suppression function to construct a discriminative feature space and utilize a deep brief network to learn spectral representation and abstraction automatically that are used as inputs to the Mahalanobis distance (MD)-based detector. In the spatial domain, the anomalies appear as a small area grouped by pixels with high correlation among them compared to BKG. Therefore, the objects appearing as a small area are extracted based on attribute filtering, and a guided filter is further employed for local smoothness. More specifically, we extract spatial features of anomalies only from one single band obtained by fusing all bands in the visible wavelength range. Finally, we detect anomalies by jointly considering the spectral and spatial detection results. Several experiments are performed, which show that our proposed method outperforms the state-of-the-art methods.

Although hyperspectral technology has continued to improve over the years, it is still limited to size, weight, and power (SWaP) constraints. One major issue is the need to sample a large number of very fine spectral bands. Such prohibitively large size of hyperpsectral data creates challenges in both data archival and processing. Compressive sensing (CS) is an enabling technology for reducing the overall data processing and SWaP requirements. This paper explores the viability of performing classification for hyperspectral data on a compressively sensed band domain (CSBD) via CS instead of the original data space, without performing sparse reconstruction. In particular, the well-known restricted isometry property (RIP) and a random spectral sampling strategy are explored for hyperspectral image classification (HSIC) in CSBD. A mathematical analysis is also presented to show that the classification error can be expressed in terms of the restricted isometry constant (RIC) so that the HSIC in the original full-band data space can be achieved in CSBD provided that sufficient band-sensing conditions are met. To validate the proposed CS-HSIC a set of real hyperspectral image experiments are performed where a commonly used spectral-spatial classification algorithm based on support vector machine (SVM) and edge-preserving filters (EPFs) is implemented for a comparative study and analysis. The results clearly demonstrate the potential of CS-HSIC in future research directions.

This paper presents a class information (CI)-based band selection (BS) approach to hyperspectral image classification (HSIC). It introduces a new concept from an information theory point of view, CI which can be used to determine an appropriate weight imposed on each class of interest. Specifically, two types of criteria, intraclass information criterion (IC) and interclass IC are derived as CI probabilities to measure CI that can be used to determine the number of training samples required to be selected for each class. With such CI-calculated probabilities, another new concept called class self-information (CSI) is also defined for each class that can be further used to define the class entropy (CE) so that CSI and CE can be used to determine the number of bands required for BS, nBS. In order to find desired nBS bands, two types of BS methods based on CSI and CE are custom-designed, called single class signature-constrained BS (SCSC-BS) which utilizes the constrained energy minimization (CEM) to constrain each individual class signature to select bands for a particular class according to its CSI-determined nBS and a multiple class signatures-constrained BS (MCSC-BS) which takes advantage of linearly constrained minimum variance (LCMV) to constrain all class signatures to select CE-determined nBS bands for all classes. These SCSC-BS and MCSC-BS selected bands are then used to perform classification and evaluated by CI-weighted classification measures by real image experiments. The results show that HSIC using judiciously selected partial bands as well as CI-weighted measures can improve HSIC with using full bands.

This paper develops a new approach to band selection for multiple-target detection, called constrained-target band selection (CTBS). Its idea is derived from the concept of constrained energy minimization (CEM) by constraining a target of interest, while minimizing the variance resulting from the background (BKG). By taking advantage of CEM, the variance produced by a target of interest can be further used as a measure of prioritizing bands as well as a means of selecting bands for this particular target. As a result, two CTBS-based band prioritization (BP) criteria, called minimal variance-based BP (MinV-BP) and maximal variance-based BP (MaxV-BP), and two CTBS-based BS methods, called sequential forward CTBS (SF-CTBS) and sequential backward CTBS (SB-CTBS), can be derived for multiple-target detection. Since the bands selected by CTBS vary with targets of interest used to constrain CEM, in order for CTBS to be applied to multiple targets, a new fusion technique, called band fusion selection (BFS), is further developed for CTBS to integrate bands selected by different targets so that CTBS can work for all targets. Unlike most BS methods for target detection which generally simultaneously select a fixed set of bands for all targets of interest, the ideas of constraining multiple-target detection and using BFS are novelty of this paper. Experimental results show that CTBS performs well for multiple-target detection.

In hyperspectral image classification (HSIC), background (BKG) is generally excluded from consideration due to the fact that obtaining complete knowledge of BKG is nearly impossible in reality. Unfortunately, BKG has significant impact on classification and band selection (BS). This paper investigates both issues and presents a novel approach called class signature-constrained BKG suppression (CSCBS) approach to BS for HSIC, where class signatures can be obtained either by a priori or a posteriori knowledge or training samples, and BKG suppression can be accomplished by taking the inverse of the sample correlation matrix R. Its idea takes advantage of the concept of the linearly constrained minimum variance (LCMV) developed from adaptive beamforming by constraining class signatures of interest while minimizing the effect caused by the unknown BKG so as to enhance the classification performance. There are two immediate applications of CSCBS. One is its application to HSIC, in which it becomes a CSCBS classifier. The other is its use of the LCMV-suppressed BKG as a measure to derive the band prioritization (BP) criteria and BS. Experimental results demonstrate that generally CSCBS does not need the full-band set for HSIC since a partial band subset selected by CSCBS-BP/BS can actually improve the classification results using full-band information.

This paper presents a new spectral-spatial (SS) approach to hyperspectral image classification (HSIC), called SS feedback close network system (SSFCNS), which has not been explored in the past. Unlike commonly used SS-based methods SSFCNS includes a feedback close network system (FCNS) to obtain spatial information via a selective spatial filter in an iterative manner. More specifically, SSFCNS takes advantage of FCNS which utilizes a particularly selected spatial filter to capture a posteriori spatial information directly from spectral-classified data samples and then feeds back such obtained spatial-filtered image to be combined with the current image cube to create a new image cube that can be used as a new input to re-implement SSFCNS. The process is carried out in such a way that the spatial information obtained from spectral classification results is updated by FCNS iteratively and terminated by a Tanimoto index (TI)-derived automatic stopping rule. To evaluate the performance of SSFCNS several spatial filters (i.e., Gaussian, bilateral, guided, and Gabor filters) are explored for real image experiments. The experimental results demonstrate that SSFCNS performs significantly better in classification accuracy compared to SS-based methods which do not use FCNS.

In hyperspectral image classification spectral information and spatial information are always integrated to improve the classification accuracy. This paper develops an iterative version of support vector machine, to be called iterative SVM (ISVM) to perform hyperspectral image classification by extracting spatial information iteratively via feedback loops. In processing ISVM an initial hyperspectral data cube is obtained by combining the original image and its first principal component. SVM is then implemented to the resulting data cube to produce an initial classification map. In each feedback loop, a Gaussian filter is applied to obtain the spatial information of the SVM-classification map so that the Gaussian-filtered map is further fed back to combine with the currently processed hyperspectral cube for the next round of iteration. As for terminating the iterative process an automatic stopping rule is also developed. To evaluate the performance of ISVM real image experiments are conducted in comparison with state-of-the-art spectral-spatial hyperspectral classification methods. The experiment results demonstrate that ISVM performed better by providing higher classification accuracy.

Phalaenopsis is a significant agriculture product with high economic value in Taiwan. However, the fusarium wilt causes Phalaenopsis leaves turning yellow, thinning, water loss, and finally died. This paper presents an emerging method to detect fusarium wilt on Phalaenopsis stem base. In order to build the detection models, the hyperspectral databases are generated form two statues of Phalaenopsis samples, which are health and disease sample. We applied band selection (BS) processing base on band prioritization (BP) and band de-correlation (BD) to extract the significant bands and eliminate the redundant bands. Then, three algorithms were used, orthogonal subspace projection (OSP), constrain energy minimization (CEM), and support vector machine (SVM) to detect the fusarium wilt.

This paper proposed an efficient height slicing method for detecting trees using a canopy height model (CHM). A digital forest simulator was proposed to randomly generate trees by a 2-dimensional Gaussian probability density function. Details such as the location, crown radius, and height of a tree are automatically generated via the parameters of location, spread blob, and amplitude of a two-dimensional Gaussian function. An index of hit rate was used to evaluate the detection power of the algorithm and the indices RMSE and PRMSE were used to evaluate the estimation accuracy of tree height and crown radius. The proposed algorithm was able to detect trees at 100% and 80% hit rate at a stand density of less than 600 trees per hectare and this then gradually decreased to 85% and 70% as stand density increased to 1000 trees per hectare for artificial forest and natural forest respectively.

This paper introduces a new concept of band capacity (BC) of a hyperspectral image and further develops a theory for BC. Its idea is derived from information theory where a band channel can be constructed from a hyperspectral image with both its channel input space and channel output space specified by its full band set and the channel transition probabilities between the input and output spaces characterized by between band discrimination. In particular, a transition probability from a spectral band in the band channel input space to a spectral band in the band channel output space is calculated by their spectral discriminatory power/probability. By virtue of such a formulated band channel, its maximal mutual information can be defined as BC of a hyperspectral image to represent spectral discriminatory power per band measured by bits. Interestingly, BC provides a key to bridging the concept of virtual dimensionality defined as the number of spectrally distinct signatures and effective band dimensionality to be used to discriminate these spectrally distinct signatures one from another. Accordingly, an immediate application of BC is to determine the number of bands to be selected, nBS. Another application is band selection with the output space specified by a selected nBS-band subset. In this case, when BC is close to one, the selected band set tends to be optimal.

Anomaly detection (AD) generally finds targets that are spectrally distinct from their surrounding neighborhoods but cannot discriminate its detected targets one from another. It cannot even perform classification because there is no prior knowledge about the data. This paper presents a new approach to AD, to be called a posteriori AD for unlabeled anomaly classification where a posteriori indicates that information obtained directly from processing data is used as new information for subsequent data processing. In particular, a posteriori AD uses a Gaussian filter to capture spatial correlation of detected anomalies as a posteriori information which is included as new information for further AD. In doing so, a posteriori AD develops an iterative version of AD, referred to as iterative anomaly detection (IAD), which implements AD by feeding back Gaussian-filtered AD maps in an iterative manner. It then uses an unsupervised target detection algorithm to identify spectrally distinct anomalies that can be used to specify particular anomaly classes. To terminate IAD, an automatic stopping rule is also derived. Finally, it uses identified distinct anomalies as desired target signatures to implement constrained energy minimization (CEM) to classify all detected anomalies into unlabeled classes. The experimental results show that a posteriori AD is indeed very effective in unlabeled anomaly classification.

This paper develops a new Neyman–Pearson detection approach, to be called band-specified virtual dimensionality (BSVD), to estimating the number of bands required by band selection (BS),$n_{\mathrm {BS}}$, as well as finding desired bands at the same time. Its idea is derived from target-specified virtual dimensionality (TSVD) where targets under hypotheses as signal sources in TSVD are replaced with bands as signal sources and the test statistics derived for a Neyman–Pearson detector (NPD) is signal-to-noise ratio (SNR) that is used to derive orthogonal subspace projection (OSP) approach for hyperspectral image classification and dimensionality reduction. Accordingly, the resulting virtual dimensionality is referred to as OSP-based BSVD. Several benefits resulting from BSVD cannot be offered by the traditional BS methods. One is its direct approach to dealing with$n_{\mathrm {BS}}$. Another is no-search strategy needed for finding optimal bands. Instead, it uses NPD to determine and rank desired bands for band prioritization. Most importantly, it determines$n_{\mathrm {BS}}$and finds desired bands simultaneously and progressively.

This paper presents an emerging method to detect pesticide residues on fruit. In order to enhance pesticide signature intensity and make the detection rate of pesticide better, we applied band weighting process and band selection (BS) process base on band prioritization (BP) and band decorrelation (BD) to adjust spectral data. Then four algorithms were used, spectral information divergence (SID), orthogonal subspace projection (OSP), constrained energy minimization (CEM), and support vector machine (SVM) to identify pesticide residues on different fruit. The results show that using CEM method has the highest detection rate of pesticide and has the potential to replace the other traditional methods.

Anomaly detection (AD) is designed to find targets that are spectrally distinct from their surrounding neighborhood. Unfortunately, commonly used anomaly detectors generally do not take into account its surrounding spatial information. This paper derives an iterative version of anomaly detection, iterative anomaly detection (IAD) to address this issue. Its idea is to use a Gaussian filter to capture spatial information of the anomaly detection map and then feeds back the Gaussian filtered AD map to create a new data cube. The whole process is repeated over again in an iterative manner. When IAD is terminated anomaly representatives are identified and can be used as desired target signatures to implement constrain energy minimization (CEM) so as to classify all detected anomalies. Accordingly, IAD can be considered as anomaly classification.

Automatic target generation process (ATGP) has been widely used for unsupervised hyperspectral target detection. It implements a succession of orthogonal subspace projections (OSPs) to extract targets of interest without prior knowledge. This paper extends ATGP to a kernel version of ATGP, called kernel ATGP (KATGP) to further deal with linear non-separation problem. It introduces nonlinear kernels to map original data space into a higher dimensional feature space so that ATGP can effectively find.

This paper extends target-constrained interference minimized filter (TCIMF) to multiclass-constrained background suppression classifier (MCBSC) for hyperspectral image classification. In order to capture spatial contextual information MCBSC makes use of a Gaussian filter to feed back a Gaussian-filtered MCBSC map to create a new set of hyperspectral images for MCBSC to be re-implemented again in an iterative manner, referred to as iterative MCBSC (IMCBSC). Finally, it uses Otsu's method to perform hyperspectral image classification. As shown by experiments, MCBSC generally performs better than existing spectral-spatial hyperspectral image classification techniques in terms of several quantitative measures, such as classification rate, false classification rate, precision rate, accuracy rate in addition to overall accuracy (OA) rate.

This letter develops a progressive band processing (PBP) of fast iterative pixel purity index (FIPPI) according to a band sequential acquisition format in such a way that FIPPI can be processed band by band, while band acquisition is ongoing. As a result, PBP-FIPPI can generate progressive profiles of interband changes among PPI counts which allow users to observe significant bands that capture PPI counts. The idea to implement PBP-FIPPI is to use an inner loop specified by skewers and an outer loop specified by bands to process FIPPI. Interestingly, these two loops can also be interchanged with an inner loop specified by bands and an outer loop iterated by growing skewers. The resulting FIPPI is called progressive skewer processing of FIPPI. It turns out that both versions provide different insights into the design of FIPPI.

This letter extends the constrained band selection (CBS) technique to constrained band subset selection (CBSS) in a similar manner that constrained energy minimization has been extended to linearly constrained minimum variance. CBSS constrains multiple bands as a band subset as opposed to CBS constraining a single band as a singleton set. To achieve this goal, CBSS requires a strategy to search for an optimal band subset, while CBS does not. In this letter, two new sequential algorithms, referred to as sequential CBSS and successive CBSS, which do not exist in CBS are derived for CBSS to find desired band subsets and to avoid exhaustive search.

This paper presents a theory of adaptive linear spectral mixture analysis (ALSMA), which can implement LSMA using an adaptive linear mixing model (ALMM) that adjusts and varies with spectral signatures adaptively. In doing so, a recursive LSMA (RLSMA) is developed for ALSMA to allow LSMA to update spectral signature by spectral signature without reprocessing LSMA and also to fuse LSMA results obtained by ALMM using different sets of spectral signatures. To form ALMM, the concept of RLSMA-specified virtual dimensionality is further proposed for ALSMA, which not only can find spectral signatures recursively by RLSMA to adjust ALMM but also can automatically determine the number of spectral signatures via Neyman-Pearson detection theory.

This paper presents a new approach, called band subset selection (BSS)-based hyperspectral anomaly detection (AD), which selects multiple bands simultaneously as a band subset rather than selecting multiple bands one at a time as the tradition band selection (BS) does, referred to as sequential multiple BS (SQMBS). Its idea is to first use virtual dimensionality (VD) to determine the number of multiple bands, nBS needed to be selected as a band subset and then develop two iterative process, sequential BSS (SQ-BSS) algorithm and successive BSS (SC-BSS) algorithm to find an optimal band subset numerically among all possible nBS combinations out of the full band set. In order to terminate the search process the averaged least-squares error (ALSE) and 3-D receiver operating characteristic (3D ROC) curves are used as stopping criteria to evaluate performance relative to AD using the full band set. Experimental results demonstrate that BSS generally performs better background suppression while maintaining target detection capability compared to target detection using full band information.

Hyperspectral image classification faces various levels of difficulty due to the use of different types of hyperspectral image data. Recently, spectral-spatial approaches have been developed by jointly taking care of spectral and spatial information. This paper presents a completely different approach from a subpixel target detection view point. It implements four stage processes, a preprocessing stage, which uses band selection (BS) and nonlinear band expansion, referred to as BS-then-nonlinear expansion (BSNE), a detection stage, which implements constrained energy minimization (CEM) to produce subpixel target maps, and an iterative stage, which develops an iterative CEM (ICEM) by applying Gaussian filters to capture spatial information, and then feeding the Gaussian-filtered CEM-detection maps back to BSNE band images to reprocess CEM in an iterative manner. Finally, in the last stage Otsu's method is applied to converting ICEM-detected real-valued maps to discrete values for classification. The entire process is called BSNE-ICEM. Experimental results demonstrate BSNE-ICEM, which has advantages over support vector machine-based approaches in many aspects, such as easy implementation, fewer parameters to be used, and better false classification and precision rates.

An information theoretical approach to multiple-band selection (MBS) is presented in this paper. It formulates a MBS problem as a channel capacity problem by considering the original band set as a channel input space and the selected multiple band set as a channel output space with the channel transition probabilities specified by band discrimination between original bands and selected bands. Then bands are selected by iteratively finding a best possible input space that yields the maximal channel capacity. As a result, there is no need of band prioritization and de-correlation generally required by traditional band selection (BS). Two iterative algorithms are developed for MBS, sequential channel capacity MBS (SQ-CCMBS) and successive channel band selection (SC-CCMBS).

Simplex growing algorithm (SGA) is an endmember finding algorithm which grows simplexes with maximal volumes one vertex at a time to find new endmembers where simplex volumes (SV) are calculated by determinants of endmember matrix. However, three issues arise in SV calculation by matrix determinants. One is excessive computation. Another is the matrix determinant-calculated SV does not generally yield true SV if the matrix is not a square matrix in which case dimensionality reduction is required. A third one is numerical instability. To resolve these issues this paper presents a new geometric approach to SGA, called geometric simplex growing algorithm (GSGA) which takes advantage of simplex geometric structures to calculate simplex volume (SV) by considering a simplex to be formed by its base and height so that SV can be calculated simply by multiplying its height with its base where the height is the magnitude of the newly generated endmember and the base is the volume of the simplex formed by previous endmembers. With such a simple geometric structure GSGA has been shown to be the best among all variants currently derived from SGA in the literature.

A recent developed band selection, called constrained band selection (CBS), makes use of constrained energy minimization (CEM) to constrain a single band to calculate its priority for band selection (BS). This paper extends such CEM-BS to a constrained multiple band selection (CMBS)-based method, to be called linearly constrained minimum variance multiple band-constrained selection (CMBS), which uses LCMV to constrain multiple bands to perform band subset selection. Since CMBS selects multiple bands as a band subset as a whole it does not require band prioritization (BP) or band de-correlation (BD) as traditional band selection (BS) usually does. However, CMBS is traded for one challenging issue, which is excessive computational complexity because it requires running through a total number of subsets in the power set of a full band set compared to BS which only needs to select one band at a time. In order to avoid exhaustive search for all band subsets in it power set, a sequential CMBS, successive CMBS (SC-CMBS) is developed to ease computational complexity.

Nowadays, the accidents of oil spill become more and more frequent, causing pollution to the natural resources, marine environment and lives in the sea. As a result, the detection of oil spill draws more and more attentions. One of the most popular region-based active contour models proposed by Chan and Vese, is widely used to image segmentation. But it can't segment hyperspectral oil spill image well, which has blurry boundaries, low distinction, and noise and so on. In order to segment oil spill region from the hyperspectral oil spill image accurately, we improved the region-based active contour model in this paper. For the energy functional, we firstly bring the thought of Fisher criterion into the fitting term to get a better classification result faster. Secondly, a new stop function based on gradient of spectral angle measurement is added into the length term, so as to take advantage of the edge information fully even it is blurry. At last, the model is extended to be able to segment desired material from the complex image with several classes in it. We take some experiments on synthetic and real hyperspectral images to verify the effectiveness of our model, and apply it to the airborne hyperspectral oil spill image. Results of the proposed model on synthetic and testing hyperspectral images show that it outperforms the CV model greatly, and does better than several other segmentation and classification algorithms. Results on hyperspectral oil spill images show that it improves the ability of distinguishing oil spills from sea water, even there are boats and flats in the image.

This paper develops a new approach to band selection (BS), called multiple band selection (MBS), which does not require band prioritization to select bands but rather relies on applications to select bands. Its idea is to first use virtual dimensionality (VD) to determine the number of multiple bands needed to be selected. Then MBS is performed by two major iterative process, sequential multiple band selection (SQ-MBS) and successive multiple band selection (SC-MBS). In order to evaluate the performance of MBS anomaly detection is used its application for demonstration.

Recursive band processing of orthogonal subspace projection (RBP-OSP) is developed according to the band sequential (BSQ) format acquired by a hyperspectral imaging sensor. It can be implemented band by band recursively without waiting for data being completely collected. This is particularly important for satellite communication when data download is limited by bandwidth and transmission. Unlike band selection which requires prior knowledge of how many bands are needed to be selected, RBP-OSP has capability which allows different process units to process data whenever bands are available. In addition, it also enables users to identify significant bands during data processing. Finally and most importantly, RBP can provide progressive profiles on OSP performance, which is the best advantage that RBP-OSP can offer and cannot be accomplished by any one-shot operator.

Automatic target generation process (ATGP) has been widely used for unsupervised target detection. However, as designed, it detects targets using full-band information. Unfortunately, on many occasions, various targets can be detected using varying bands, and ATGP can only provide one-shot target detection with all bands being used. This paper develops a new approach which can implement ATGP bandwise in a progressive manner, called progressive band processing of ATGP (PBP-ATGP) so that ATGP can be carried out band by band. Since PBP-ATGP must repeatedly implement orthogonal projections, recursive equations are further derived for PBP-ATGP, to be called recursive band processing of ATGP (RBP-ATGP) which can implement PBP-ATGP recursively. As a result, many advantages can be benefited from RBP-ATGP. Most importantly, RBP-ATGP can generate 3-D interband progressive profiles from band to band that can be used for progressive target detection, a task for which no target detection techniques using full-band information can provide.

The simplex growing algorithm (SGA) has been widely used for finding endmembers. It can be considered as a sequential version of the well-known endmember finding algorithm, N-finder algorithm (N-FINDR), which finds endmembers one at a time by growing simplexes. However, one of the major hurdles for N-FINDR and SGA is the calculation of simplex volume (SV) which poses a great challenge in designing any algorithm using SV as a criterion for finding endmembers. This paper develops an orthogonal projection (OP)-based SGA (OP-SGA) which essentially resolves this computational issue. It converts the issue of calculating SV to calculating the OP on previously found simplexes without computing matrix determinants. Most importantly, a recursive Kalman filter-like OP-SGA, to be called recursive OP-SGA (ROP-SGA), can be also derived to ease computation. By virtue of ROP-SGA, several advantages and benefits in computational savings and hardware implementation can be gained for which N-FINDR and SGA do not have.

This paper develops band weighting spectral methods, which are wSAM and wSID, for detection of pesticide residues on vegetables. Since the water content of vegetables has significant impact on the measured spectrum, the proposed band weighting measures are able to suppress the effect of water content to enhance detectability of of pesticide residue detection. Compared to the traditional band selection techniques, there are three advantages. First of all, it does not require determining the number of bands to be selected. Second, the proposed methods assigned a weight to each band based on the amount of pesticide information. Third, the band weighting method could help reduce the effect of undesired signal, which is the water content in our case. The experimental study further demonstrates the utilities of our proposed band weighting methods.

Automatic target generation process (ATGP) has been used in a wide range of applications in hyperspectral image analysis. It performs a sequence of orthogonal subspace projections to extract potential targets of interest. This letter presents a recursive version of the ATGP, which is referred to as the recursive ATGP (RATGP) and has three advantages over the ATGP as follows: 1) there is no need of inverting a matrix as the ATGP does for finding each new target; 2) there is a significant reduction in the computational complexity in the hardware design due to its recursive structure; and 3) there is an automatic stopping rule that can be derived by the Neyman-Pearson detection theory to terminate the algorithm.

Constrained energy minimization (CEM) has been widely used for subpixel detection. It takes advantage of inverting the global sample correlation matrix R to suppress background so as to enhance detection of targets of interest. This paper presents a progressive band processing of CEM (PBP-CEM) which can perform CEM for target detection progressively band by band according to band sequential format. In doing so, a new concept, called causal band correlation matrix (CBCM), is introduced to replace the global sample correlation matrix R. It is a global correlation matrix formed by only those bands that were already visited up to the band currently being processed while excluding bands yet to be visited in the future. The proposed PBP-CEM allows CEM to be processed whenever bands are available, without waiting for completing band collection. With such an advantage, CEM has potential in data transmission and communication, specifically in satellite data processing.

Orthogonal subspace projection (OSP) has found many applications in hyperspectral data exploitation. Its effectiveness and usefulness result from implementation of two stage processes, i.e., annihilation of undesired signal sources by an OSP via inverting a matrix in the first stage followed by a matched filter to extract the desired signal source in the second stage. This paper presents a theory of recursive OSP (ROSP) for hyperspectral imaging, which performs OSP recursively without inverting undesired signature matrices. This ROSP opens up many new dimensions in extending OSP. First of all, ROSP allows OSP to implement varying signatures via a recursive equation without reinverting undesired signature matrices. Second, ROSP can be further used to derive an unsupervised ROSP (UROSP) OSP, which allows OSP to find a growing number of unknown signal sources recursively while simultaneously determining a desired number of signal sources. As a result, the commonly used automatic target generation process (ATGP) can be extended to a recursive ATGP, which can be considered as a special case of UROSP. Third, for practical applications, UROSP can be also extended in two differ ent fashions to causal process and progressive process, which give rise to causal UROSP and progressive UROSP, respectively, both of which can be easily realized in hardware implementation. Finally, UROSP provides a feasible stopping rule via a recently developed UROSP-specified virtual dimensionality.

Linear spectral mixture analysis (LSMA) generally performs with signatures assumed to be known to form a linear mixing model to be known. Unfortunately, this is generally not the case in real world applications. An unsupervised fully constrained least squares (UFCLS) method has been proposed to find these desired signatures. Unfortunately, it requires prior knowledge about the number of signatures, p needed to be generated. The recently proposed virtual dimensionality (VD) can be used for this purpose. This paper develops a recursive UFCLS (RUFCLS) method to accomplish these two tasks in one-shot operation, viz., determine the value of p as well as find these p signatures simultaneously. Such RUFCLS can perform data unmixing progressively signature-by-signature via a recursive update equation with signatures used to form a linear mixing model for linear spectral unmixing generated by UFCLS. Most importantly, RUFCLS does not require any matrix inverse operation but only matrix multiplications and outer products of vectors. This significant advantage provides an effective computational means of determining the VD.

Automatic target generation process (ATGP) has been found very useful and effective for unsupervised target detection. It performs a sequence of orthogonal subspace projection to extract potential targets of interest. One major issue arises in ATGP is how to terminate the algorithm in the sense that how many targets are required for ATGP to generate before it is terminated. This paper presents a recursive version of ATGP, referred to as recursive ATGP (RATGP) which has two advantages. One is no need of inverting any matrix as ATGP does for finding each target. Most importantly, a stopping rule can be derived for ATGP via RATGP is also developed using the Neyman-Pearosn detection theory to determine how many targets needed to be generated by RATGP before it is terminated.

This paper revisits a well-known fully constrained least squares (FCLS) method developed by Heinz and Chang and develops an approach to finding analytical solutions to FCLS, called analytical FCLS (AFCLS) which can be solved in closed forms instead of FCLS being solved by numerically algorithms. As a result, the AFCLS-unmixed results using analytical solutions are more accurate than FCLS-unmixed results resulting from numerical solutions.

Orthogonal subspace projection (OSP) requires inverting a matrix to eliminate effect of unwanted signal sources on unmixing of desired signal sources. When the number of such wanted signals sources is large, which is indeed the case for hyperspectra data, OSP will become slow due to its matrix inversion. This paper develops a simple alternative approach to OSP without computing matrix inversion, called Gram Schmidt orthogonal vector projection (GSOVP) which is also based on orthogonal projection. Instead of annihilating all unwanted signal sources and then extracting the desired signal as OSP does, GSOVP accomplishes these two tasks by simple inner products. As a result, computational complexity is significantly reduced and hardware design is further simplified.

Anomaly detection using sliding windows is not new but using sliding causal windows has not been explored in the past. The need of causality arises from real time processing where the used sliding windows should not include future data samples that have not been visited, i.e., data samples come in after the currently being processed data sample. This paper develops an approach to anomaly detection using sliding causal windows that has capability of being implemented in real time. In doing so two types of causal windows are defined, causal matrix window and causal array window from which a causal sample covariance/correlation matrix can be derived. As for the causal array window recursive update equations are also derived and thus, speed up real time processing.

One key issue encountered in endmember extraction is to determine the number of endmembers, p, required to be extracted. Virtual dimensionality (VD) has been widely used for this purpose. However, VD was originally developed and defined as the number of spectrally distinct signatures which are not necessarily pure signatures. So, on some occasions the VD estimated value for p may not be accurate to be used for the number of endmembers. This paper develops an endmember-specified VD (ES-VD) which makes use of data sample vectors generated by a specific endemember finding algorithm (EFA) as target signal sources and then determine if these signal sources are indeed true endmember by a binary composite hypothesis testing to determine endmembers. As a result, ES-VD varies with different target signal sources produced by EFAs. Most importantly, ES-VD not only determines the value of VD and in the mean time it also finds desired endmembers.

A new band selection (BS), called progressive BS (PBS) of spectral unmixing for hyperspectral imagery is being presented. It is quite different from the traditional BS in the sense that the former adapts the number of selected bands, p to various endmembers used for spectral unmixing, while the latter fixes the value of p at a constant for all endmembers. Due to the fact that different endmembers post various levels of difficulty in discrimination, each endmember should have its own custom-selected bands to specify its spectral characteristics. In order to address this issue, p is composed of two values, one value determined by virtual dimensionality to accommodate each of endmembers and the other is determined by a new concept of band dimensionality allocation to account for discrminability among endmembers. In order to find appropriate bands to be used for PBS, band prioritization and band de-correlation are included to rank bands according to significance of band information and to remove interband redundancy, respectively. As a result, spectral unmixing can be performed progressively by selecting different bands for various endmembers, a task that the traditional BS cannot accomplish. The effectiveness and advantages of using PBS over BS are also demonstrated by experiments.

Virtual dimensionality (VD) has received considerable interest in its use of specifying the number of spectrally distinct signatures present in hyperspectral data. Unfortunately, it never defines what such a signature is. For example, various targets of interest, such as anomalies and endmembers, should be considered as different types of spectrally distinct signatures and have their own different values of VD. Specifically, these targets are insignificant in terms of signal energies due to their relatively small populations. Accordingly, their contributions to second-order statistics (2OS) are rather limited. In this case, 2OS-based methods such as eigen-approaches to determine VD may not be effective in determining how many such type of signal sources as spectrally distinct signatures are. This paper develops a new theory that expands 2OS-VD theory to a high-order statistics (HOS)-based VD, called HOS-VD theory. Since there is no counterpart of the characteristic polynomial equation used to find eigenvalues in 2OS available for HOS, a direct extension is inapplicable. This paper re-invents a wheel by finding actual targets directly from the data rather than eigenvectors/singular vectors used in 2OS-VD theory which do not represent any real targets in the data. Consequently, comparing to 2OS-VD theory which can only be used to estimate the value of VD without finding real targets, the developed HOS-VD theory can accomplish both of tasks at the same time, i.e., determining the value of VD as well as finding actual targets directly from the data.

Band selection (BS) has advantages over data dimensionality in satellite communication and data transmission. However, several issues regarding real time processing need to be addressed, (1) how many bands required for BS, (2) how to select appropriate bands, (3) how to take advantage of previously selected bands without re-implementing BS, and finally and most important, (4) how to tune bands to be selected in real time as number of bands varies. This paper presents a new approach, called progressive band processing (PBP) for Modified Fully Abundance-Constrained Spectral Unmixing (MFCLS) without actually implementing BS. When spectral unmixing is performed, BS must be done prior to data unmixing in which case real time implementation in data communication is infeasible. The proposed PBP-MFCLS allows users to incorporate new incoming bands into data unmixing currently being processed. Accordingly, PBP-MFCLS can be carried out band by band in a real time and progressive fashion with unmixed data updated recursively band by band in the same way that data is processed by a Kalman filter.

N-finder algorithm (N-FINDR) has been widely used for endmember extraction in hyperspectral imagery. Due to its high computational complexity, developing fast computing N-FINDR has received considerable interest, specifically to take advantage of field-programmable gate array (FPGA) architecture in hardware implementation to realize N-FINDR. However, there are two severe drawbacks arising in the nature of N-FINDR design, the number of endmembers,p, which must be fixed once its value is determined in FPGA design and inconsistency in final extracted endmembers caused by different selections of initial endmembers. This paper investigates a progressive version of N-FINDR, previously known as simplex growing algorithm for its FPGA implementation which can resolve these two issues.

Radial basis function (RBF) has been widely used in kernel-based approaches. This paper extended RBF kernels to weighted RBF (WRBF) kernels by introducing a weighting matrix A into RBF kernels. A key to success in implementing WRBF kernels is to design different appropriate weighting matrices to implement WRBF kernels. Three weighting matrices are of particular interest, covariance matrix, correlation matrix and within-class scatter matrix. Experimental results via various applications show that classifiers using WRBF kernels provide better performance than that using un-weigheted RBF kernels.

Linear spectral mixture analysis (LSMA) has been widely used in remote sensing community for spectral unmixing. This letter develops a promising technique, called kernel-based LSMA (KLSMA), which uses nonlinear kernels to resolve the issue of nonlinear separability arising in unmixing and further extends several commonly used LSMA techniques to their kernel-based counterparts. Interestingly, according to experiments conducted for real hyperspectral and multispectral images, KLSMA is more effective than LSMA when data samples are heavily mixed.

Support vector machine (SVM) has received considerable interest in hyperspectral image classification. In order to make SVM work effectively one challenge is selection of training samples. In supervised classification it is generally done by random sampling for cross validation where two issues must be addressed. One is how many training samples required to allow SVM to produce good performance and the other is how to deal with random selections of training samples which produce inconsistent results. This paper presents a new type of SVM, called iterative SVM (ISVM) to address these two issues. The idea is to implement an SVM iteratively in such a way that the sample size is not necessarily to be large while the random sampling issue can be also resolved. To substantiate the utility of ISVM Purdue data is further used for experiments.

This paper presents a new BS, called dynamic BS (DBS) which revolutionizes the commonly used BS by considering the number of bands to be selected, p as a variable which varies with criterion used for BS and different applications. Its idea is derived from information theory where it assumes that signal sources are considered as source alphabets with probabilities being their mutual spectral discriminatory powers calculated by a spectral similarity measure. If we further assume that a signal source is accommodated by a particular spectral band, the signal source will be encoded by 1 indicating a band being used to specify the signal source and 0 otherwise. Accordingly, band dimensionality to discriminate a signal source from other sources can be determined by its variable coding length obtained by the Huffman coding. With this interpretation the conventional BS can be considered as a fixed-dimensionality BS, referred to as static BS(SBS).

Two of the most challenging issues in the unsupervised linear spectral mixture analysis (ULSMA) are: 1) determining the number of signatures to form a linear mixing model; and 2) finding the signatures used to unmix data. These two issues do not occur in supervised LSMA since the target signatures are assumed to be known a priori. With recent advances in hyperspectral sensor technology, many unknown and subtle signal sources can now be uncovered and revealed and such signal sources generally cannot be identified by prior knowledge. Even when they can, the obtained knowledge may not be reliable, accurate, or complete. As a consequence, the resulting unmixed results may be misleading. This paper addresses these issues by introducing a new concept of inter-band spectral information (IBSI), which can be used to categorize signatures into background and target classes in terms of their sample spectral statistics. It then develops a component analysis (CA)-based ULSMA where two classes of signatures can be extracted directly from the data by two different CA-based transforms without requiring prior knowledge. In order to substantiate the utility of the proposed approach, synthetic images are used for experiments and real images are further used for validation.

N-finder algorithm (N-FINDR) has been widely used in endmember extraction. When it comes to implementation several issues need to be addressed. One is determination of endmembers, p required for N-FINDR to generate. Another is its computational complexity resulting from an exhaustive search. A third one is its requirement of dimensionality reduction. A fourth and probably the most critical issue is its use of random initial endmembers which results in inconsistent final endmember selection and results are not reproducible. This paper re-invents the wheel by re-designing the N-FINDR in such a way that all the above-mentioned issues can be resolved while making the last issue an advantage. The idea is to implement the N-FINDR as a random algorithm, called random N-FINDR (RN-FINDR) so that a single run using one set of random initial endmembers is considered as one realization. If there is an endmember present in the data, it should appear in any realization regardless of what random set of initial endmembers is used. In this case, the N-FINDR is terminated when the intersection of all realizations produced by two consecutive runs of RN-FINDR remains the same in which case the p is then automatically determined by the intersection set without appealing for any criterion. In order to substantiate the proposed RN-FINDR custom-designed synthetic image experiments with complete knowledge are conducted for validation and real image experiments are also performed to demonstrate its utility in applications.

Virtual dimensionality (VD) was originally developed for estimating the number of spectrally distinct signatures present in hyperspectral data. The effectiveness of the VD is determined by the technique used for VD estimation. This paper develops an orthogonal subspace projection (OSP) technique to estimate the VD. The idea is derived from linear spectral mixture analysis. A similar idea was also previously investigated by the signal subspace estimate (SSE) and later improved by hyperspectral signal subspace identification by minimum error (HySime). Interestingly, with an appropriate interpretation the proposed OSP technique includes the SSE/HySime as its special case. In order to demonstrate its utility experiments using synthetic images and real image data sets are conducted for performance analysis.

Endmember extraction has received increasing interest in hyperspectral image analysis. One widely used endmember extraction algorithm is pixel purity index (PPI), which finds endmembers via a set of random vectors, called skewers. Several issues arise in its implementation. One is the prior knowledge of the number of skewersKrequired to be used. Second, due to random nature in skewers, the final results are inconsistent and unreproducible. Third, it needs to know the number of dimensions to be retained after dimensionality reduction. Fourth, it needs to preset a cutoff threshold to extract potential endmembers. Finally, it involves human intervention to manually select final endmembers. This letter derives a random PPI (RPPI) to resolve the aforementioned issues. It considers the result produced by PPI using a random set of initial vectors as skewers as a realization of a random algorithm. From a statistical signal processing view point, if endmembers are crucial in terms of information, they should occur in realizations produced by PPI regardless of what set is chosen for skewers. By virtue of this assumption, the proposed RPPI is developed and validated by experiments.

The simplex growing algorithm (SGA) was recently developed as an alternative to the N-finder algorithm (N-FINDR) and shown to be a promising endmember extraction technique. This paper further extends the SGA to a versatile real-time (RT) processing algorithm, referred to as RT SGA, which can effectively address the following four major issues arising in the practical implementation for N-FINDR: (1) use of random initial endmembers which causes inconsistent final results; (2) high computational complexity which results from an exhaustive search for finding all endmembers simultaneously; (3) requirement of dimensionality reduction because of large data volumes; and (4) lack of RT capability. In addition to the aforementioned advantages, the proposed RT SGA can also be implemented by various criteria in endmember extraction other than the maximum simplex volume.

Virtual dimensionality (VD) is a new concept which was originally developed for estimating the number of spectrally distinct signatures present in hyperspectral data. The effectiveness of the VD is determined by the technique used for VD estimation. This paper develops an orthogonal subspace projection (OSP) technique to estimate the VD. The idea is derived from linear spectral mixture analysis where a data sample vector is modeled as a linear mixture of a finite set of what is called as virtual endmembers in this paper. A similar idea was also previously investigated by the signal subspace estimate (SSE) and was later improved by hyperspectral signal subspace identification by minimum error (HySime), where the minimum mean squared error is used as a criterion to determine the VD. Interestingly, with an appropriate interpretation, the proposed OSP technique includes the SSE/HySime as its special case. In order to demonstrate its utility, experiments using synthetic images and real image data sets are conducted for performance analysis.

The purpose of this study is to present a new method, independent vector analysis (IVA), by extending independent component analysis (ICA) of univariate source signals to multivariate source signals on Magnetic Resonance Imaging (MRI). IVA is utilized to relief the limitation of the conventional ICA approach. The proposed method can resolve the permutation problem during individual ICA runs for group brain MR images. The proposed IVA method in conjunction with support vector machine (SVM), we can effectively separate the different part of gray, white matter and cerebrospinal fluid (CSF) from brain soft tissues. In order to demonstrate the proposed IVA-SVM method, experiments are conducted for performance analysis and evaluation. Simulation results show that using IVA can greatly release from the problem cause from traditional ICA to the situation of analyzing inconsistent results of MR image.

Simplex growing algorithm (SGA) was recently developed as an alternative to the N-finder algorithm (N-FINDR) which is shown to be a promising endmember extraction technique. This paper further extends the SGA to a real-time processing algorithm, referred to as real-time SGA (RT SGA) that can effectively address four major issues arising in practical implementation for N-FINDR, (1) use of random initial endmembers which causes inconsistent final results, (2) very high computational complexity which results from an exhaustive search for finding all endmembers simultaneously, (3) requirement of dimensionality reduction because of enormous data volumes to be processed and (4) lack of real-time capability.

A recent paper by Changdevelops a new algorithm, called the simplex growing algorithm, which has shown promise in endmember extraction. There is an erroneous description made for one of synthetic image experiments. While making a simple correction would have sufficed, a series of studies has led to interesting and intriguing results on how to determine an appropriate number of endmembers$p$, how to design a better endmember extraction algorithm, and how to use an effective technique to perform dimensionality reduction.

Knee-related injuries including meniscal tears are common in both young athletes and the aging population, and require accurate diagnosis and surgical intervention when appropriate. With proper techniques and radiologists' experienced skills, confidence in detection of meniscal tears can be quite high. This paper develops a novel computer-aided detection (CAD) diagnostic system for automatic detection of meniscal tears in the knee. Evaluation of this CAD system using an archived database of images from 40 individuals with suspected knee injuries indicates that the sensitivity and specificity of the proposed CAD system are 83.87% and 75.19%, respectively, compared to the mean sensitivity and specificity of 77.41% and 81.39%, respectively, obtained by experienced radiologists in routine diagnosis without using the CAD. The experimental results suggest that the developed CAD system has great potential and promise in automatic detection of both simple and complex meniscal tears of the knee.

Anomaly detection is of particular interest in hyperspectral image analysis since many unknown and subtle signals which cannot be resolved by multispectral sensors can now be uncovered by hyperspectral imagers. More importantly, the signals of this type generally cannot be identified by visual assessment or prior knowledge and provide crucial and critical information for data analysis. Many anomaly detectors have been designed based on the most widely used anomaly detector developed by Reed and Yu, called RX detector (RXD). However, a key issue in making RX detector-like anomaly detectors successful is how to effectively utilize the information provided by the sample correlation, e.g., sample covariance matrix used by RXD. This paper develops a concept of designing anomaly detectors which includes RXD-like anomaly detectors as special cases. It is referred to as multiple-window anomaly detection (MWAD) which makes use of multiple windows with varying sizes to capture different levels of local spectral variations so that anomalous targets of various sizes can be characterized and interpreted by different window sizes. With this new MWAD, many interesting findings can be derived including the RXD-like anomaly detectors as its special cases.

Principal components analysis (PCA) is probably the most commonly used transform to perform various tasks in many applications. It produces a set of uncorrelated components according to decreasing magnitude of eigenvalues of a second order-statistics covariance matrix. This paper presents four variants of PCA from an algorithmic implementation aspect, SiMultaneous PCA (SMPCA), ProGressive PCA (PGPCA), Successive PCA (SCPCA) and PRioritized PCA (PRPCA). Except the SMPCA which is the commonly used PCA, all the other three are new developments of the PCA, each of which has its own merits and has not been explored in the literature.

One of commonly used criteria for finding an endmember set is to assume that for a given number of endmembers, p, a p-vertex simplex with its vertices specified by p endmembers always yields the maximum volume. Since there are also other criteria which have been widely used for endmember extraction, the issue of interest is "does an endmember set really produce a simplex with maximum volume?" In other words, using the criterion of a simplex with maximum volume is a better and more effective measure than other criteria currently being used by endmember extraction such as orthogonal projection-based pixel purity index (PPI), fully constrained least squares-based spectral unmixing, etc. This paper explores this issue by investigating a number of popular endmember extraction algorithms which are designed by different criteria. An extensive experiment-based study is also conducted for comparative analysis.

This paper presents a novel band selection-based feature characterization technique for a hyperspectral signature, which is referred to as variable-number variable-band selection (VNVBS). Since a hyperspectral signature can be uniquely characterized by its spectral profile, its feature characterization can be achieved by selecting appropriate bands from the original set of spectral bands, and the number of bands to be selected is totally determined by its original spectral shape. As a result, two hyperspectral signatures may require different sets of bands for spectral feature characterization. Therefore, the proposed VNVBS allows one to select a different number of variable bands in accordance with the hyperspectral signature to be processed. In order for the VNVBS to select an appropriate subset of bands for a hyperspectral signature, a new band prioritization criterion (BPC), which is referred to as orthogonal subspace projector based BPC, is derived. It assigns a different priority score to each spectral band of a hyperspectral signature such that various features can be captured by the VNVBS. Accordingly, the VNVBS can be interpreted as a spectral feature extraction technique for hyperspectral signature characterization. Finally, experiments using two data sets are conducted to demonstrate that the VNVBS can improve the performance of the hyperspectral signature characterization.

The pixel purity index (PPI) has been widely used in hyperspectral image analysis for endmember extraction due to its publicity and availability in the Environment for Visualizing Images (ENVI) software. Unfortunately, its detailed implementation has never been made available in the literature. This paper investigates the PPI based on limited published results and proposes a fast iterative algorithm to implement the PPI, referred to as fast iterative PPI (FIPPI). It improves the PPI in several aspects. Instead of using randomly generated vectors as initial endmembers, the FIPPI produces an appropriate initial set of endmembers to speed up its process. Additionally, it estimates the number of endmembers required to be generated by a recently developed concept, virtual dimensionality (VD) which is one of the most crucial issues in the implementation of PPI. Furthermore, it is an iterative algorithm, where an iterative rule is developed to improve each of the iterations until it reaches a final set of endmembers. Most importantly, it is an unsupervised algorithm as opposed to the PPI, which requires human intervention to manually select a final set of endmembers. The experiments show that both the FIPPI and the PPI produce very close results, but the FIPPI converges very rapidly with significant savings in computation.

Automated extraction of spectral endmembers is a crucial task in hyperspectral data analysis. In most cases, the computational complexity of endmember extraction algorithms is very high, in particular, for very high-dimensional datasets. However, the intrinsic properties of available techniques are amenable to the design of parallel implementations. In this letter, we evaluate several parallel algorithms that represent three representative approaches to the problem of extracting endmembers. Two parallel algorithms have been selected to represent a first class of algorithms based on convex geometry concepts. In particular, we develop parallel implementations of approximate versions of the N-FINDR and pixel purity index algorithms, along with a parallel hybrid of both techniques. A second class is given by algorithms based on constrained error minimization and represented by a parallel version of the iterative error analysis algorithm. Finally, a parallel version of the automated morphological endmember extraction algorithm is also presented and discussed. This algorithm integrates the spatial and spectral information as opposed to the other discussed algorithms, a feature that introduces additional considerations for its parallelization. The proposed algorithms are quantitatively compared and assessed in terms of both endmember extraction accuracy and parallel efficiency, using standard AVIRIS hyperspectral datasets. Performance data are measured on Thunderhead, a parallel supercomputer at NASA's Goddard Space Flight Center.

Linear spectral mixture analysis (LSMA) has been used in a wide range of applications. It is generally implemented without constraints due to mathematical tractability. However, it has been shown that constrained LSMA can improve unconstrained LSMA, specifically in quantification when accurate estimates of abundance fractions are necessary. As constrained LSMA is considered, two constraints are generally imposed on abundance fractions, abundance sum-to-one constraint (ASC) and abundance nonnegativity constraint (ANC), referred to as abundance-constrained LSMA (AC-LSMA). A general and common approach to solving AC-LSMA is to estimate abundance fractions in the sense of least squares error (LSE) while satisfying the imposed constraints. Since the LSE resulting from each individual band in abundance estimation is not weighted in accordance with significance of bands, the effect caused by the LSE is then assumed to be uniform over all the bands, which is generally not necessarily true. This paper extends the commonly used AC-LSMA to three types of weighted AC-LSMA resulting from three different signal processing perspectives, parameter estimation, pattern classification, and orthogonal subspace projection. As demonstrated by experiments, the weighted AC-LSMA generally performs better than unweighted AC-LSMA which can be considered as a special case of our proposed weighted AC-LSMA with the weighting matrix chosen to be the identity matrix.

Linear spectral mixture analysis (LSMA) has been widely used in subpixel analysis and mixed-pixel classification. One commonly used approach is based on either the least square error (LSE) criterion such as least squares LSMA or the signal-to-noise ratio (SNR) such as orthogonal subspace projection (OSP). Unfortunately, it is known that such criteria are not necessarily optimal for pattern classification. This paper presents a new and alternative approach to LSMA, called Fisher's LSMA (FLSMA). It extends the well-known pure-pixel-based Fisher's linear discriminant analysis to LSMA. Interestingly, what can be done for the LSMA can be also developed for the FLSMA. Of particular interest are two types of constraints imposed on the LSMA, target signature-constrained LSMA and target abundance-constrained LSMA, which can be also derived in parallel for the FLSMA, to be called feature-vector-constrained FLSMA (FVC-FLSMA) and abundance-constrained FLSMA (AC-FLSMA), respectively. Since Fisher's ratio used by the FLSMA is a more appropriate classification criterion than the LSE or SNR used for the LSMA, the FVC-FLSMA improves over the classical least squares based LSMA and SNR-based OSP in mixed-pixel classification. Similarly, the AC-FLSMA also improves abundance-constrained least squares based LSMA in quantification of abundance fractions.

Constrained energy minimization (CEM) has shown effective in hyperspectral target detection. It linearly constrains a desired target signature while minimizing interfering effects caused by other unknown signatures. This paper explores this idea for band selection and develops a new approach to band selection, referred to as constrained band selection (CBS) for hyperspectral imagery. It interprets a band image as a desired target signature vector while considering other band images as unknown signature vectors. As a result, the proposed CBS using the concept of the CEM to linearly constrain a band image, while also minimizing band correlation or dependence provided by other band images, is referred to as CEM-CBS. Four different criteria referred to as Band Correlation Minimization (BCM), Band Correlation Constraint (BCC), Band Dependence Constraint (BDC), and Band Dependence Minimization (BDM) are derived for CEM-CBS.. Since dimensionality resulting from conversion of a band image to a vector may be huge, the CEM-CBS is further reinterpreted as linearly constrained minimum variance (LCMV)-based CBS by constraining a band image as a matrix where the same four criteria, BCM, BCC, BDC, and BDM, can be also used for LCMV-CBS. In order to determine the number of bands required to select p, a recently developed concept, called virtual dimensionality, is used to estimate the p. Once the p is determined, a set of p desired bands can be selected by the CEM/LCMV-CBS. Finally, experiments are conducted to substantiate the proposed CEM/LCMV-CBS four criteria, BCM, BCC, BDC, and BDM, in comparison with variance-based band selection, information divergence-based band selection, and uniform band selection.

A new growing method for simplex-based endmember extraction algorithms (EEAs), called simplex growing algorithm (SGA), is presented in this paper. It is a sequential algorithm to find a simplex with the maximum volume every time a new vertex is added. In order to terminate this algorithm a recently developed concept, virtual dimensionality (VD), is implemented as a stopping rule to determine the number of vertices required for the algorithm to generate. The SGA improves one commonly used EEA, the N-finder algorithm (N-FINDR) developed by Winter, by including a process of growing simplexes one vertex at a time until it reaches a desired number of vertices estimated by the VD, which results in a tremendous reduction of computational complexity. Additionally, it also judiciously selects an appropriate initial vector to avoid a dilemma caused by the use of random vectors as its initial condition in the N-FINDR where the N-FINDR generally produces different sets of final endmembers if different sets of randomly generated initial endmembers are used. In order to demonstrate the performance of the proposed SGA, the N-FINDR and two other EEAs, pixel purity index, and vertex component analysis are used for comparison.

In this paper, spectral unmixing methods, which are extensively used in hyperspectral imaging area, are proposed for classification and abundance fraction (concentration) estimation of chemical and biological agents that exist in the mixture form. Several government-furnished datasets, which were collected through the infrared spectrum method, were thoroughly analyzed. Two similarity measures-the spectral angle mapper and spectral information divergence-were investigated in order to provide a quantitative comparison basis with respect to the performance of the applied spectral unmixing methods in the existence of similar and distinct agents. The use of the similarity measures provided valuable information about the signature characteristics of the agents, which led to a better understanding about the capabilities of the investigated methods. The orthogonal subspace projection (OSP) method was investigated as the first unmixing, classification, and abundance estimation technique. It was observed that the OSP method provided good results when the number of agents in the database was small and was composed of distinct agents. However, when the number of agents was incremented by adding agents that share similar characteristics, the abundance estimation accuracy gradually degraded in addition to generating negative abundance fraction estimates. The second investigated unmixing method was called nonnegatively constrained least squares (NCLS). The results and analyses indicated that the NCLS method outperformed the OSP approach by providing considerably more accurate fraction estimates while at the same time not generating any negative fraction estimates; thus, the use of the NCLS method was found to be promising in detection and abundance fraction estimation of chemical and biological agents that exist in the form of mixtures. In addition, efficient implementation of NCLS has resulted in much lower computations than the conventional OSP implementation.

Many endmember extraction algorithms (EEAs) have been developed to find endmembers that are assumed to be pure signatures in hyperspectral data. However, two issues arising in EEAs have not been addressed: one is the knowledge of the number of endmembers that must be provideda priori, and the other is the initialization of EEAs, where most EEAs initialize their endmember-searching processes by using randomly generated endmembers, which generally result in inconsistent final selected endmembers. Unfortunately, there has been no previous work reported on how to address these two issues, i.e., how to select a set of appropriate initial endmembers and how to determine the number of endmembers p. This paper takes up these two issues and describes two-stage processes to improve EEAs. First, a recently developed concept of virtual dimensionality (VD) is used to determine how many endmembers are needed to be generated for an EEA. Experiments show that the VD is an adequate measure for estimating p. Second, since EEAs are sensitive to initial endmembers, a properly selected set of initial endmembers can make significant improvements on the searching process. In doing so, a new concept of endmember initialization algorithm (EIA) is thus proposed, and four different algorithms are suggested for this purpose. It is surprisingly found that many EIA-generated initial endmembers turn out to be the final desired endmembers. A further objective is to demonstrate that EEAs implemented in conjunction with EIA-generated initial endmembers can significantly reduce the number of endmember replacements as well as the computing time during endmember search

In hyperspectral image analysis, the principal components analysis (PCA) and the maximum noise fraction (MNF) are most commonly used techniques for dimensionality reduction (DR), referred to as PCA-DR and MNF-DR, respectively. The criteria used by the PCA-DR and the MNF-DR are data variance and signal-to-noise ratio (SNR) which are designed to measure data second-order statistics. This paper presents an independent component analysis (ICA) approach to DR, to be called ICA-DR which uses mutual information as a criterion to measure data statistical independency that exceeds second-order statistics. As a result, the ICA-DR can capture information that cannot be retained or preserved by second-order statistics-based DR techniques. In order for the ICA-DR to perform effectively, the virtual dimensionality (VD) is introduced to estimate number of dimensions needed to be retained as opposed to the energy percentage that has been used by the PCA-DR and MNF-DR to determine energies contributed by signal sources and noise. Since there is no prioritization among components generated by the ICA-DR due to the use of random initial projection vectors, we further develop criteria and algorithms to measure the significance of information contained in each of ICA-generated components for component prioritization. Finally, a comparative study and analysis is conducted among the three DR techniques, PCA-DR, MNF-DR, and ICA-DR in two applications, endmember extraction and data compression where the proposed ICA-DR has been shown to provide advantages over the PCA-DR and MNF-DR.

Independent component analysis (ICA) has shown success in many applications. This paper investigates a new application of the ICA in endmember extraction and abundance quantification for hyperspectral imagery. An endmember is generally referred to as an idealized pure signature for a class whose presence is considered to be rare. When it occurs, it may not appear in large population. In this case, the commonly used principal components analysis may not be effective since endmembers usually contribute very little in statistics to data variance. In order to substantiate the author's findings, an ICA-based approach, called ICA-based abundance quantification algorithm (ICA-AQA) is developed. Three novelties result from the author's proposed ICA-AQA. First, unlike the commonly used least squares abundance-constrained linear spectral mixture analysis (ACLSMA) which is a second-order statistics-based method, the ICA-AQA is a high-order statistics-based technique. Second, due to the use of statistical independency, it is generally thought that the ICA cannot be implemented as a constrained method. The ICA-AQA shows otherwise. Third, in order for the ACLSMA to perform the abundance quantification, it requires an algorithm to find image endmembers first then followed by an abundance-constrained algorithm for quantification. As opposed to such a two-stage process, the ICA-AQA can accomplish endmember extraction and abundance quantification simultaneously in one-shot operation. Experimental results demonstrate that the ICA-AQA performs at least comparably to abundance-constrained methods

The orthogonal subspace projection (OSP) approach has received considerable interest in hyperspectral data exploitation recently. It has been shown to be a versatile technique for a wide range of applications. Unfortunately, insights into its design rationale have not been investigated and have yet to be explored. This work conducts a comprehensive study and analysis on the OSP from several signal processing perspectives and further discusses in depth how to effectively operate the OSP using different levels of a priori target knowledge for target detection and classification. Additionally, it looks into various assumptions made in the OSP and analyzes filters with different forms, some of which turn out to be well-known and popular target detectors and classifiers. It also shows how the OSP is related to the well-known least-squares-based linear spectral mixture analysis and how the OSP takes advantage of Gaussian noise to arrive at the Gaussian maximum-likelihood detector/estimator and likelihood ratio test. Extensive experiments are also included in this paper to simulate various scenarios to illustrate the utility of the OSP operating under various assumptions and different degrees of target knowledge.

A texture analysis approach of using an improved texture feature coding method (TFCM) and the support vector machines (SVM) for target detection is presented. Preliminary tests on mammograms showed over 88% of normal mammograms and 85% of abnormal mammograms were correctly identified. Automatic target detection with a cascade-sliding-window (CSW) technique is also discussed.

Spectral measures have been used in material identification and discrimination. They are effective if the spectral signatures are calibrated and not contaminated. However, it may not be true in many real applications, specifically, for mixed pixels and subpixel targets. This paper investigates the issue of discrimination and identification for subpixel targets and further develops sample spectral covariance/correlation matrix-based hyperspectral measures to account for spectral variability within subpixel targets. Two types of measures are of interest and studied, Mahalanobis distance-based hyperspectral measures and matched filter-based hyperspectral measures. In order to substantiate the proposed measures, a real data-based comparative analysis is conducted and compared to two spectral similarity measures, spectral angle mapper (SAM) and spectral information divergence (SID) for performance evaluation. The experiments show that both Mahalanobis distance-based hyperspectral measures and matched filter-based hyperspectral measures work very effectively and outperformed the SAM and the SID in discrimination and identification for subpixel targets.

Texture is one of important features of masses in mammograms. A recent texture unit-based texture spectrum approach, referred to as texture unit coding (TUC) has shown promise in texture classification. This paper presents a new application of the TUC to mass classification in mammograms. The TUC generates a texture spectrum for a texture image that can be used to describe the characteristics of masses. It also develops an information divergence (ID)-based discrimination criterion to measure the discrepancy between two texture spectra, a concept yet to explore in texture analysis. The TUC along with ID are further applied to mass classification in mammograms where the minimammographic database provided by the Mammographic Image Analysis Society (MIAS) is used for experiments.

Anomaly detection finds target pixels whose signatures are spectrally distinct from their surrounding pixels. It is generally performed without prior knowledge. This work presents an adaptive causal anomaly detector (ACAD) which implements a causal anomaly detector in such a fashion that a target pixel will be removed from the data correlation matrix once it is detected as an anomaly. As a result, it improves the commonly used RX algorithm as well as a recently developed causal RX filter.

A great challenge of hyperspectral target detection is to detect subtle targets without prior knowledge, particularly, when the targets of interest are insignificant and occur with low probabilities. This work provides a promising alternative to adaptive hyperspectral target detection. It considers a nested spatial window-based target detection (NSWTD) approach for hyperspectral imagery where a set of different spatial windows are nested and implemented to extract targets whose signatures are spectrally and spatially distinct. The use of nested spatial windows is determined by the image pixel resolution and applications. In order to demonstrate the performance of the proposed NSWTD approach, dual nested windows and three nested windows are implemented for computer simulations and real hyperspectral image experiments. The experimental results demonstrate that our proposed NSWTD approach performs effectively and improves a recent adaptive anomaly detector developed by Kwon et al. and the commonly used anomaly detector developed by Reed and Yu, referred to as RX algorithm. Its computation complexity is also very simple.

Orthogonal subspace projection (OSP) has received considerable interest in hyperspectral image classification. It performs well when the complete knowledge of image endmembers is available. In reality, obtaining such prior knowledge is very difficult, if not impossible. This work investigates a variant of OSP, called uniform projection (UP) and presents a UP-based unsupervised algorithm for hyperspectral image classification. It first implements a uniform target detector (UTD) to find a set of interfering signatures, I, then another uniform I-annihilated detector (UIAD) to find desired target signatures. The signatures in I are combined with the UIAD found desired signatures to form a target signatures matrix M which can be used for supervised image classification. In this case, OSP can be used for this purpose. In order to demonstrate the utility of the proposed unsupervised classification technique for hyperspectral imagery, a series of computer simulations and experiments are conducted for analysis.

With very high spectral resolution, hyperspectral sensors can now uncover many unknown signal sources which cannot be identified by visual inspection or a priori. In order to account for such unknown signal sources, we introduce a new definition, referred to as virtual dimensionality (VD) in this paper. It is defined as the minimum number of spectrally distinct signal sources that characterize the hyperspectral data from the perspective view of target detection and classification. It is different from the commonly used intrinsic dimensionality (ID) in the sense that the signal sources are determined by the proposed VD based only on their distinct spectral properties. These signal sources may include unknown interfering sources, which cannot be identified by prior knowledge. With this new definition, three Neyman-Pearson detection theory-based thresholding methods are developed to determine the VD of hyperspectral imagery, where eigenvalues are used to measure signal energies in a detection model. In order to evaluate the performance of the proposed methods, two information criteria, an information criterion (AIC) and minimum description length (MDL), and the factor analysis-based method proposed by Malinowski, are considered for comparative analysis. As demonstrated in computer simulations, all the methods and criteria studied in this paper may work effectively when noise is independent identically distributed. This is, unfortunately, not true when some of them are applied to real image data. Experiments show that all the three eigenthresholding based methods (i.e., the Harsanyi-Farrand-Chang (HFC), the noise-whitened HFC (NWHFC), and the noise subspace projection (NSP) methods) produce more reliable estimates of VD compared to the AIC, MDL, and Malinowski's empirical indicator function, which generally overestimate VD significantly. In summary, three contributions are made in this paper, 1) an introduction of the new definition of VD, 2) three Neyman-Pearson detection theory-based thresholding methods, HFC, NWHFC, and NSP derived for VD estimation, and 3) experiments that show the AIC and MDL commonly used in passive array processing and the second-order statistic-based Malinowski's method are not effective measures in VD estimation.

One of the challenges in remote sensing image processing is subpixel detection where the target size is smaller than the ground sampling distance, therefore, embedded in a single pixel. Under such a circumstance, these targets can be only detected spectrally at the subpixel level, not spatially as ordinarily conducted by classical image processing techniques. This paper investigates a more challenging issue than subpixel detection, which is the estimation of target size at the subpixel level. More specifically, when a subpixel target is detected, we would like to know "what is the size of this particular target within the pixel?". The proposed approach is to estimate the abundance fraction of a subpixel target present in a pixel, then find what portion it contributes to the pixel that can be used to determine the size of the subpixel target by multiplying the ground sampling distance. In order to make our idea work, the subpixel target abundance fraction must be accurately estimated to truly reflect the portion of a subpixel target occupied within a pixel. So, a fully constrained linear unmixing method is required to reliably estimate the abundance fractions of a subpixel target for its size estimation. In this paper, a recently developed fully constrained least squares linear unmixing is used for this purpose. Experiments are conducted to demonstrate the utility of the proposed method in comparison with an unconstrained linear unmixing method, unconstrained least squares method, two partially constrained least square linear unmixing methods, sum-to-one constrained least squares, and nonnegativity constrained least squares.

A hyperspectral imaging sensor can reveal and uncover targets with very narrow diagnostic wavelengths. However, it comes at a price that it can also extract many unknown signal sources such as background and natural signatures as well as unwanted man-made objects, which cannot be identified visually or a priori. These unknown signal sources can be referred to as interferers, which generally play a more dominant role than noise in hyperspectral image analysis. Separating such interferers from signals and annihilating them subsequently prior to detection may be a more realistic approach. In many applications, the signals of interest can be further divided into desired signals for which we want to extract and undesired signals for which we want to eliminate to enhance signal detectability. This paper presents a signal-decomposed and interference-annihilated (SDIA) approach in applications of hyperspectral target detection. It treats interferers and undesired signals as separate signal sources that can be eliminated prior to target detection. In doing so, a signal-decomposed interference/noise (SDIN) model is suggested in this paper. With the proposed SDIN model, the orthogonal subspace projection-based model and the signal/background/noise model can be included as its special cases. As shown in the experiments, the SDIN model-based SDIA approach generally can improve the performance of the commonly used generalized-likelihood ratio test and constrained energy minimization approach on target detection and classification.

Thresholding color video images is challenging because of the low spatial resolution and the complex backgrounds. This paper investigates the issue of thresholding these images by reducing the number of colors in order to improve automated text detection and recognition. An unsupervised thresholding approach is presented which reduces the background complexity while retaining the important text character pixels. The experiments show that our proposed thresholding approach performs significantly better than simple image histogram-based methods which generally do not produce satisfactory results.

Thresholding color video images is challenging because of the low spatial resolution and the complex backgrounds. This paper investigates the issue of thresholding these images by reducing the number of colors in order to improve automated text detection and recognition. An unsupervised thresholding approach is presented which reduces the background complexity while retaining the important text character pixels. The experiments show that our proposed thresholding approach performs significantly better than simple image histogram-based methods, which generally do not produce satisfactory results.

We conduct a comparative study and investigate the relationship between two well-known techniques in hyperspectral image detection and classification: orthogonal subspace projection (OSP) and constrained energy minimization. It is shown that they are closely related and essentially equivalent provided that the noise is white with large SNR. Based on this relationship, the performance of OSP can be improved via data-whitening and noise-whitening processes.

This paper presents a new spectral signature detection approach to magnetic resonance (MR) image classification. It is called constrained energy minimization (CEM) method, which is derived from the minimum variance distortionless response in passive sensor array processing. It considers a bank of spectral channels as an array of sensors where each spectral channel represents a sensor and object spectral signature in multispectral MR images are viewed as signals impinging upon the array. The strength of the CEM lies on its ability in detection of spectral signatures of interest without knowing image background. The detected spectral signatures are then used for classification. The CEM makes use of a finite impulse response (FIR) filter to linearly constrain a desired object while minimizing interfering effects caused by other unknown signal sources. Unlike most spatial-based classification techniques, the proposed CEM takes advantage of spectral characteristics to achieve object detection and classification. A series of experiments is conducted and compared with the commonly used c-means method for performance evaluation. The results show that the CEM method is a promising and effective spectral technique for MR image classification.

Mixed pixel classification is different from spatial-based image classification in the sense that the former deals with abundance fractional images resulting from mixed pixels as opposed to classification maps produced by the latter. As a result, mixed pixel classification is generally carried out by visual inspection on the generated abundance fractional images. Consequently, it can be very subjective and vary with different human interpretations. Under such circumstance, it is difficult to substantiate an algorithm and conducting a comparative analysis is impossible. This paper presents one histogram-based approach to thresholding abundance fractional images. It thresholds an abundance fractional image into a binary image using a probability of confidence as a threshold value.

Orthogonal subspace projection (OSP) and generalized likelihood ratio test (GLRT) have shown success in hyperspectral image classification. The OSP is derived by maximizing signal-to-noise ratio (SNR) resulting from a linear mixture model in which the noise is assumed to be white. On the other hand, the GLRT is formulated based on a signal detection model that can be described by a binary hypothesis testing problem. In order for the GLRT to derive an analytical form, the noise in the signal detection model is generally assumed to be white Gaussian noise. However, Gaussianity is generally not true in remotely sensed imagery. Interestingly, such assumption has not been investigated. This paper presents a comparative study between OSP and GLRT based on their assumptions. In particular, a detailed analysis of assumptions made on these two approaches is conducted through a series of computer simulations. Experimental results show that the OSP does not depend on Gaussian noise. By the contrast, the GLRT is affected by the Gaussian noise assumption. If it is violated, its performance is degraded.

The commonly used linear spectral unmixing is generally performed on a single pixel basis and does not take advantage of inter-pixel spatial correlation. The Kalman filter has been considered to extend the linear unmixing by taking into account both spectral and spatial correlation. In addition to a linear mixture model implemented as a measurement equation, it includes a state equation to keep track of changes in between pixels. However, Kalman filtering requires the complete knowledge of image endmembers present in image data, which is generally not available and very difficult to obtain a priori. In order to relax this dilemma, this paper presents an unsupervised Kalman filtering (UKF) approach to signature estimation for remotely sensed images. It first uses an anomaly detector combined with orthogonal subspace projection (OSP) to extract desired image endmember signatures directly from the image data, then further applies a discrimination measure to classify the extracted signatures into a set of distinct signatures that will be used in the measurement equation. In order for the UKF to effectively capture spatial correlation among sample image pixels, the state equation is also implemented dynamically to adjust the state transition matrix adaptively. Experimental results have shown that the proposed UKF approach provides additional advantages over the commonly used spectral-based linear unmixing methods.

Linear spectral mixture analysis has been widely used for subpixel detection and mixed pixel classification. When it is implemented as constrained LSMA, the constraints are generally imposed on abundance fractions in the mixture. In this paper, we consider an alternative approach, which imposes constraints on target signature vectors rather than target abundance fractions. The idea is to constrain directions of target signature vectors of interest in two different ways. One, referred to as linearly constrained minimum variance approach develops a linear filter to constrain these target signature vectors along preassigned directions using a set of specific filter gains while minimizing the filter output variance. Another, referred to as the linearly constrained discriminant analysis (LCDA), is derived from Fisher's linear discriminant analysis, but constrains the Fisher's discriminant vectors along predetermined directions to improve classification performance. Recently, Bowles et al. introduced another target signature-constrained approach, referred to as filter-vectors method, which requires a linear mixture model to implement constraints on target signature vectors. Interestingly, it turns out that the filter-vectors method can be considered as a special version of both linearly constrained minimum variance and linearly constrained discriminant analysis approaches.

Anomaly detection becomes increasingly important in hyperspectral image analysis, since hyperspectral imagers can now uncover many material substances which were previously unresolved by multispectral sensors. Two types of anomaly detection are of interest and considered in this paper. One was previously developed by Reed and Yu to detect targets whose signatures are distinct from their surroundings. Another was designed to detect targets with low probabilities in an unknown image scene. Interestingly, they both operate the same form as does a matched filter. Moreover, they can be implemented in real-time processing, provided that the sample covariance matrix is replaced by the sample correlation matrix. One disadvantage of an anomaly detector is the lack of ability to discriminate the detected targets from another. In order to resolve this problem, the concept of target discrimination measures is introduced to cluster different types of anomalies into separate target classes. By using these class means as target information, the detected anomalies can be further classified. With inclusion of target discrimination in anomaly detection, anomaly classification can be implemented in a three-stage process, first by anomaly detection to find potential targets, followed by target discrimination to cluster the detected anomalies into separate target classes, and concluded by a classifier to achieve target classification. Experiments show that anomaly classification performs very differently from anomaly detection.

Independent component analysis (ICA) has shown success in blind source separation and channel equalization. Its applications to remotely sensed images have been investigated in recent years. Linear spectral mixture analysis (LSMA) has been widely used for subpixel detection and mixed pixel classification. It models an image pixel as a linear mixture of materials present in an image where the material abundance fractions are assumed to be unknown and nonrandom parameters. This paper considers an application of ICA to the LSMA, referred to as ICA-based linear spectral random mixture analysis (LSRMA), which describes an image pixel as a random source resulting from a random composition of multiple spectral signatures of distinct materials in the image. It differs from the LSMA in that the abundance fractions of the material spectral signatures in the LSRMA are now considered to be unknown but random independent signal sources. Two major advantages result from the LSRMA. First, it does not require prior knowledge of the materials to be used in the linear mixture model, as required for the LSMA. Second, and most importantly, the LSRMA models the abundance fraction of each material spectral signature as an independent random signal source so that the spectral variability of materials can be described by their corresponding abundance fractions and captured more effectively in a stochastic manner.

The authors present a linearly constrained minimum variance (TCMV) beamforming approach to real time processing algorithms for target detection and classification in hyperspectral imagery. The only required knowledge for these LCMV-based algorithms is targets of interest. The idea is to design a finite impulse response (FIR) filter to pass through these targets using a set of linear constraints while also minimizing the variance resulting from unknown signal sources. Two particular LCMV-based target detectors, the constrained energy minimization (CEM) and the target-constrained interference-minimization filter (TCIMF), are presented. In order to expand the ability of the LCMV-based target detectors to classification, the LCMV approach is further generalized so that the targets can be detected and classified simultaneously. By taking advantage of the LCMV-based filter structure, the LCMV-based target detectors and classifiers can be implemented by a QR-decomposition and be processed line-by-line in real time. The experiments using HYDICE and AVIRIS data are conducted to demonstrate their real time implementation.

The authors present a projection pursuit (PP) approach to target detection. Unlike most of developed target detection algorithms that require statistical models such as linear mixture, the proposed PP is to project a high dimensional data set into a low dimensional data space while retaining desired information of interest. It utilizes a projection index to explore projections of interestingness. For target detection applications in hyperspectral imagery, an interesting structure of an image scene is the one caused by man-made targets in a large unknown background. Such targets can be viewed as anomalies in an image scene due to the fact that their size is relatively small compared to their background surroundings. As a result, detecting small targets in an unknown image scene is reduced to finding the outliers of background distributions. It is known that "skewness," is defined by normalized third moment of the sample distribution, measures the asymmetry of the distribution and "kurtosis" is defined by normalized fourth moment of the sample distribution measures the flatness of the distribution. They both are susceptible to outliers. So, using skewness and kurtosis as a base to design a projection index may be effective for target detection. In order to find an optimal projection index, an evolutionary algorithm is also developed to avoid trapping local optima. The hyperspectral image experiments show that the proposed PP method provides an effective means for target detection.

A radial basis function neural network (RBFNN) is developed to examine two mixing models, linear and nonlinear spectral mixtures, which describe the spectra collected by both airborne and laboratory-based spectrometers. The authors examine the possibility that there may be naturally occurring situations where the typically used linear model may not provide the most accurate resultant spectral description. Under such a circumstance, a nonlinear model may better describe the mixing mechanism.

Linear spectral mixture analysis (LSMA) is a widely used technique in remote sensing to estimate abundance fractions of materials present in an image pixel. In order for an LSMA-based estimator to produce accurate amounts of material abundance, it generally requires two constraints imposed on the linear mixture model used in LSMA, which are the abundance sum-to-one constraint and the abundance nonnegativity constraint. The first constraint requires the sum of the abundance fractions of materials present in an image pixel to be one and the second imposes a constraint that these abundance fractions be nonnegative. While the first constraint is easy to deal with, the second constraint is difficult to implement since it results in a set of inequalities and can only be solved by numerical methods. Consequently, most LSMA-based methods are unconstrained and produce solutions that do not necessarily reflect the true abundance fractions of materials. In this case, they can only be used for the purposes of material detection, discrimination, and classification, but not for material quantification. The authors present a fully constrained least squares (FCLS) linear spectral mixture analysis method for material quantification. Since no closed form can be derived for this method, an efficient algorithm is developed to yield optimal solutions. In order to further apply the designed algorithm to unknown image scenes, an unsupervised least squares error (LSE)-based method is also proposed to extend the FCLS method in an unsupervised manner.

Target detection in remotely sensed images can be conducted spatially, spectrally or both. The difficulty of detecting targets in remotely sensed images with spatial image analysis arises from the fact that the ground sampling distance is generally larger than the size of targets of interest in which case targets are embedded in a single pixel and cannot be detected spatially. Under this circumstance target detection must be carried out at subpixel level and spectral analysis offers a valuable alternative. In this paper, the problem of subpixel spectral detection of targets in remote sensing images is considered, where two constrained target detection approaches are studied and compared. One is a target abundance-constrained approach, referred to as nonnegatively constrained least squares (NCLS) method. It is a constrained least squares spectral mixture analysis method which implements a nonnegativity constraint on the abundance fractions of targets of interest. Another is a target signature-constrained approach, called constrained energy minimization (CEM) method. It constrains the desired target signature with a specific gain while minimizing effects caused by other unknown signatures. A quantitative study is conducted to analyze the advantages and disadvantages of both methods. Some suggestions are further proposed to mitigate their disadvantages.

Over the past years, many algorithms have been developed for multispectral and hyperspectral image classification. A general approach to mixed pixel classification is linear spectral unmixing, which uses a linear mixture model to estimate the abundance fractions of signatures within a mixed pixel. As a result, the images generated for classification are usually gray scale images, where the gray level value of a pixel represents a combined amount of the abundance of spectral signatures residing in this pixel. Due to a lack of standardized data, these mixed pixel algorithms have not been rigorously compared using a unified framework. The authors present a comparative study of some popular classification algorithms through a standardized HYDICE data set with a custom-designed detection and classification criterion. The algorithms to be considered for this study are those developed for spectral unmixing, the orthogonal subspace projection (OSP), maximum likelihood, minimum distance, and Fisher's linear discriminant analysis (LDA). In order to compare mixed pixel classification algorithms against pure pixel classification algorithms, the mixed pixels are converted to pure ones by a designed mixed-to-pure pixel converter. The standardized HYDICE data are then used to evaluate the performance of various pure and mixed pixel classification algorithms. Since all targets in the HYDICE image scenes can be spatially located to pixel level, the experimental results can be presented by tallies of the number of targets detected and classified for quantitative analysis.

Principal components analysis (PCA) is effective at compressing information in multivariate data sets by computing orthogonal projections that maximize the amount of data variance. Unfortunately, information content in hyperspectral images does not always coincide with such projections. The authors propose an application of projection pursuit (PP), which seeks to find a set of projections that are "interesting," in the sense that they deviate from the Gaussian distribution assumption. Once these projections are obtained, they can be used for image compression, segmentation, or enhancement for visual analysis. To find these projections, a two-step iterative process is followed where they first search for a projection that maximizes a projection index based on the information divergence of the projection's estimated probability distribution from the Gaussian distribution and then reduce the rank by projecting the data onto the subspace orthogonal to the previous projections. To calculate each projection, they use a simplified approach to maximizing the projection index, which does not require an optimization algorithm. It searches for a solution by obtaining a set of candidate projections from the data and choosing the one with the highest projection index. The effectiveness of this method is demonstrated through simulated examples as well as data from the hyperspectral digital imagery collection experiment (HYDICE) and the spatially enhanced broadband array spectrograph system (SEBASS).

Orthogonal subspace projection (OSP) has been successfully applied in hyperspectral image processing. In order for the OSP to be effective, the number of bands must be no less than that of signatures to be classified. This ensures that there are sufficient dimensions to accommodate orthogonal projections resulting from the individual signatures. Such inherent constraint is not an issue for hyperspectral images since they generally have hundreds of bands, which is more than the number of signatures resident within images. However, this may not be true for multispectral images where the number of signatures to be classified is greater than the number of bands such as three-band pour l'observation de la terra (SPOT) images. This paper presents a generalization of the OSP called generalized OSP (GOSP) that relaxes this constraint in such a manner that the OSP can be extended to multispectral image processing in an unsupervised fashion. The idea of the GOSP is to create a new set of additional bands that are generated nonlinearly from original multispectral bands prior to the OSP classification. It is then followed by an unsupervised OSP classifier called automatic target detection and classification algorithm (ATDCA). The effectiveness of the proposed GOSP is evaluated by SPOT and Landsat TM images. The experimental results show that the GOSP significantly improves the classification performance of the OSP.

A hyperspectral image can be considered as an image cube where the third dimension is the spectral domain represented by hundreds of spectral wavelengths. As a result, a hyperspectral image pixel is actually a column vector with dimension equal to the number of spectral bands and contains valuable spectral information that can be used to account for pixel variability, similarity and discrimination. We present a new hyperspectral measure, the spectral information measure (SIM), to describe spectral variability and two criteria, spectral information divergence and spectral discriminatory probability for spectral similarity and discrimination, respectively. The spectral information measure is an information-theoretic measure which treats each pixel as a random variable using its spectral signature histogram as the desired probability distribution. Spectral information divergence (SID) compares the similarity between two pixels by measuring the probabilistic discrepancy between two corresponding spectral signatures. The spectral discriminatory probability calculates spectral probabilities of a spectral database (library) relative to a pixel to be identified so as to achieve material identification. In order to compare the discriminatory power of one spectral measure relative to another, a criterion is also introduced for performance evaluation, which is based on the power of discriminating one pixel from another relative to a reference pixel. The experimental results demonstrate that the new hyperspectral measure can characterize spectral variability more effectively than the commonly used spectral angle mapper (SAM).

A new application for RBF neural networks in nonlinear mixed pixel classification for hyperspectral imaging is presented. It is a three-layer neural network with the input layer specified by spectral signatures of a mixed pixel vector, the hidden layer used for nonlinear mixing functions and the output layer used to produce classification results of the mixed pixel vector. A noise estimation method in conjunction with noise subspace projection is developed to reliably estimate the member of mixing materials plus interference signatures that can be used as the number of hidden nodes as well as the member of input nodes. The least-mean-square learning algorithm is applied to adjust parameters used in the hidden layer and weights of the output layers adaptively and simultaneously so as to achieve best possible performance. The performance is evaluated through a series of experiments via AVIRIS data. A comparative analysis is also conducted among various methods.

Subpixel detection and classification are important in identification and quantification of multicomponent mixtures in remotely sensed data, such as multispectral/hyperspectral images. A recently proposed orthogonal subspace projection (OSP) has shown some success in Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and Hyperspectral Digital Imagery Collection Experiment (HYDICE) data. However, like most techniques, OSP has its own constraints. One inherent limitation is that the number of signatures to be classified cannot be greater than that of spectral bands. Owing to this limitation, OSP may not perform well for multispectral imagery as it does for hyperspectral imagery. This phenomenon is observed by three-band Satellite Pour l'Observation de la Terra (SPOT) data because of an insufficient number of spectral bands compared to the number of materials to be classified. Further, most approaches proposed for multispectral and hyperspectral image analysis, including OSP, operate on a pixel by pixel basis. In this case, a general assumption is made on the fact that the image data are stationary and pixel independent. Unfortunately, this may be true for laboratory data, but not for real data, due to varying atmospheric and scattering effects. In this paper, a Kalman filtering approach is presented that overcomes the aforementioned problems. In addition to the observation process described by a linear mixture model, a Kalman filter utilizes an abundance state equation to model the nonstationary nature in signature abundance. As a result, the signature abundance can be estimated and updated recursively by the Kalman filter and an abrupt change in signature abundance can be detected via the abundance state equation.

The goal of principal components analysis (PCA) is to find principal components in accordance with maximum variance of a data matrix. However, it has been shown recently that such variance-based principal components may not adequately represent image quality. As a result, a modified PCA approach based on maximization of SNR was proposed. Called maximum noise fraction (MNF) transformation or noise-adjusted principal components (NAPC) transform, it arranges principal components in decreasing order of image quality rather than variance. One of the major disadvantages of this approach is that the noise covariance matrix must be estimated accurately from the data a priori. Another is that the factor of interference is not taken into account in MNF or NAPC in which the interfering effect tends to be more serious than noise in hyperspectral images. In this paper, these two problems are addressed by considering the interference as a separate, unknown signal source, from which an interference and noise-adjusted principal components analysis (INAPCA) can be developed in a manner similar to the one from which the NAPC was derived. Two approaches are proposed for the INAPCA, referred to as signal to interference plus noise ratio-based principal components analysis (SINR-PCA) and interference-annihilated noise-whitened principal components analysis (IANW-PCA). It is shown that if interference is taken care of properly, SINR-PCA and IANW-PCA significantly improve NAPC. In addition, interference annihilation also improves the estimation of the noise covariance matrix. All of these results are compared with NAPC and PCA and are demonstrated by HYDICE data.

Band selection for remotely sensed image data is an effective means to mitigate the curse of dimensionality. Many criteria have been suggested in the past for optimal band selection. In this paper, a joint band-prioritization and band-decorrelation approach to band selection is considered for hyperspectral image classification. The proposed band prioritization is a method based on the eigen (spectral) decomposition of a matrix from which a loading-factors matrix can be constructed for band prioritization via the corresponding eigenvalues and eigenvectors. Two approaches are presented, principal components analysis (PCA)-based criteria and classification-based criteria. The former includes the maximum-variance PCA and maximum SNR PCA, whereas the latter derives the minimum misclassification canonical analysis (MMCA) (i.e., Fisher's discriminant analysis) and subspace projection-based criteria. Since the band prioritization does not take spectral correlation into account, an information-theoretic criterion called divergence is used for band decorrelation. Finally, the band selection can then be done by an eigenanalysis based band prioritization in conjunction with a divergence-based band decorrelation. It is shown that the proposed band-selection method effectively eliminates a great number of insignificant bands. Surprisingly, the experiments show that with a proper band selection, less than 0.1 of the total number of bands can achieve comparable performance using the number of full bands. This further demonstrates that the band selection can significantly reduce data volume so as to achieve data compression.

A new approach to multispectral and hyperspectral image analysis is presented. This method, called convex cone analysis (CCA), is based on the bet that some physical quantities such as radiance are nonnegative. The vectors formed by discrete radiance spectra are linear combinations of nonnegative components, and they lie inside a nonnegative, convex region. The object of CCA is to find the boundary points of this region, which can be used as endmember spectra for unmixing or as target vectors for classification. To implement this concept, the authors find the eigenvectors of the sample spectral correlation matrix of the image. Given the number of endmembers or classes, they select as many eigenvectors corresponding to the largest eigenvalues. These eigenvectors are used as a basis to form linear combinations that have only nonnegative elements, and thus they lie inside a convex cone. The vertices of the convex cone will be those points whose spectral vector contains as many zero elements as the number of eigenvectors minus one. Accordingly, a mixed pixel can be decomposed by identifying the vertices that were used to form its spectrum. An algorithm for finding the convex cone boundaries is presented, and applications to unsupervised unmixing and classification are demonstrated with simulated data as well as experimental data from the hyperspectral digital imagery collection experiment (HYDICE).

Function approximation has been found in many applications. The radial basis function (RBF) network is one approach which has shown a great promise in this sort of problems because of its faster learning capacity. A traditional RBF network takes Gaussian functions as its basis functions and adopts the least-squares criterion as the objective function, However, it still suffers from two major problems. First, it is difficult to use Gaussian functions to approximate constant values. If a function has nearly constant values in some intervals, the RBF network will be found inefficient in approximating these values. Second, when the training patterns incur a large error, the network will interpolate these training patterns incorrectly. In order to cope with these problems, an RBF network is proposed in this paper which is based on sequences of sigmoidal functions and a robust objective function. The former replaces the Gaussian functions as the basis function of the network so that constant-valued functions can be approximated accurately by an RBF network, while the latter is used to restrain the influence of large errors. Compared with traditional RBF networks, the proposed network demonstrates the following advantages: (1) better capability of approximation to underlying functions; (2) faster learning speed; (3) better size of network; (4) high robustness to outliers.

A recent short communication, J. J. Settle (1996), showed that an orthogonal subspace projection (OSP) classifier developed for hyperspectral image classification in J. Harsanyi et al. (1994) was equivalent to a maximum likelihood estimator (MLE) resulting from a standard method of linear unmixing. It further concluded that the MLE subsumed the OSP classifier in spite of a constant difference in their magnitudes. Coincidentally, the equivalence of the OSP approach to linear unmixing was also derived in J. Harsanyi (1993) and T. M. Tu et al. (1997) by using the least-squares estimation with the same abundance estimate given by the MLE. In this communication, the author shows, on the contrary, that the MLE can be viewed as an a posteriori version of the OSP classifier and, thus, belongs to a family of OSP-based classifiers. More importantly, the author further shows that the constant produced by the MLE determines abundance estimation and has nothing to do with classification. As a result, it only alters the abundance concentration of the classified pixels, but not classification results.

A noise subspace projection (NSP) approach to extraction and subpixel detection of target signatures in an unknown background is presented. The proposed NSP approach is derived from a recently developed subspace orthogonal projection (OSP) method and can be shown to be approximated by an adaptive filter with the optimal weight given by the Wiener-Hopf equation. As a result, the operator resulting from the NSP approach can be used as an OSP operator for scene classification and subpixel detection, on one hand, and also implemented as an adaptive filter, on the other. These advantages make the NSP approach very attractive in practical applications. In particular, the NSP operator takes advantage of the noise subspace projection to prevent from inverting correlation matrices, as required by an adaptive filter.

Classification for high-dimensional remotely sensed data generally requires a large set of data samples and enormous processing time, particularly for hyperspectral image data. In this paper, the authors present a fast two-stage classification method composed of a band selection (BS) algorithm with feature extraction/selection (FSE) followed by a recursive maximum likelihood classifier (MLC). The first stage is to develop a BS algorithm coupled with FSE for data dimensionality reduction. The second stage is to design a fast recursive MLC (RMLC) so as to achieve computational efficiency. The experimental results show that the proposed recursive MLC, in conjunction with BS and FSE, reduces computing time significantly by a factor ranging from 30 to 145, as compared to the conventional MLC.

One of the primary goals of imaging spectrometry in Earth remote sensing applications is to determine identities and abundances of surface materials. In a recent study, an orthogonal subspace projection (OSP) was proposed for image classification. However, it was developed for an a priori linear spectral mixture model which did not take advantage of a posteriori knowledge of observations. In this paper, an a posterior least squares orthogonal subspace projection (LSOSP) derived from OSP is presented on the basis of an a posteriori model so that the abundances of signatures can be estimated through observations rather than assumed to be known as in the a priori model. In order to evaluate the OSP and LSOSP approaches, a Neyman-Pearson detection theory is developed where a receiver operating characteristic (ROC) curve is used for performance analysis. In particular, a locally optimal Neyman-Pearson's detector is also designed for the case where the global abundance is very small with energy close to zero a case to which both LSOSP and OSP cannot be applied. It is shown through computer simulations that the presented LSOSP approach significantly improves the performance of OSP.

This paper will briefly describe local entropy and local relative entropy thresholding methods and compare them to two studied methods from the literature, those of Kittler and Illingworth (1986) and of Otsu (1979).

Most applications of hyperspectral imagery require processing techniques which achieve two fundamental goals: 1) detect and classify the constituent materials for each pixel in the scene; 2) reduce the data volume/dimensionality, without loss of critical information, so that it can be processed efficiently and assimilated by a human analyst. The authors describe a technique which simultaneously reduces the data dimensionality, suppresses undesired or interfering spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel vector onto a subspace which is orthogonal to the undesired signatures. This operation is an optimal interference suppression process in the least squares sense. Once the interfering signatures have been nulled, projecting the residual onto the signature of interest maximizes the signal-to-noise ratio and results in a single component image that represents a classification for the signature of interest. The orthogonal subspace projection (OSP) operator can be extended to k-signatures of interest, thus reducing the dimensionality of k and classifying the hyperspectral image simultaneously. The approach is applicable to both spectrally pure as well as mixed pixels.>

A complete sufficient statistic is presented for the class of all finite-state, finite-order stationary discrete Markov processes. This sufficient statistic is complete in the sense that it summarizes in entirety the whole of the relevant information supplied by any process sample. The sufficient statistic has application to source coding problems such as source matching and calculation of the rate distortion function.>

The source matching problem is to find the minimax codes that minimize the maximum redundancies over classes of sources where relative entropy (cross entropy, discrimination information) is adopted as a criterion to measure the redundancy. The convergence of a simple approach different from L.D. Davisson and A. Leon-Garcia's (1980) algorithm for finding such minimax codes is presented and shown. This approach is applied as an example to the class of first-order discrete Markov sources. The sufficient statistic previously used by D.H. Lee (1983) in his attempt to produce results for the first-order Markov source matching problem is corrected. A computational complexity analysis and a numerical study further demonstrate that this simple algorithm significantly reduces the required computing time, when compared to Davisson and Leon-Garcia's algorithm.>

Two iterative minimax algorithms are presented with associated convergence theorems. Both algorithms consist of iterative procedures based on a sequence of finite parameter sets. In general, these finite parameter sets are subsets of an infinite parameter space. To show their applicabilities, several commonly used examples are presented. It is also shown that minimax problems with or without finite parameter sets can be solved by these two algorithms numerically to any assigned degree of accuracy.>

A surprising resemblance has been found between the Remez and Chang-Davisson algorithm in the sense that the underlying idea accidentally coincides although the applications are quite different. The authors investigate the analogy between these algorithms. In particular, they look into their respective properties and differences and discuss their prospects. A comparison is then made to see their common structure and to gain insight into possible applications. It is concluded that one potential connection is to open up a new approach to digital filter design.>

A version of the Arimoto-Blahut algorithm for continuous channels involves evaluating integrals over an entire input space and thus is not tractable. Two generalized discrete versions of the Arimoto-Blahut algorithm are presented for this purpose. Instead of calculating integrals, both algorithms require only the computation of a sequence of finite sums. This significantly reduces numerical computational complexity.>