Local Spectral Unmixing (LSU) methods perform the unmixing of hyperspectral data locally in regions of the image. The endmembers and their abundances in each pixel are extracted region-wise, instead of globally to mitigate spectral variability effects, which are less severe locally. However, it requires the local estimation of the number of endmembers to use. Algorithms for intrinsic dimensionality (ID) estimation tend to overestimate the local ID, especially in small regions. The ID only provides an upper bound of the application and scale dependent number of endmembers, which leads to extract irrelevant signatures as local endmembers, associated with meaningless local abundances. We propose a method to select in each region the best subset of the locally extracted endmembers. Collaborative sparsity is used to detect spurious endmembers in each region and only keep the most influent ones. We compute an algorithmic regularization path for this problem, giving access to the sequence of successive active sets of endmembers when the regularization parameter is increased. Finally, we select the optimal set in the sense of the Bayesian Information Criterion (BIC), favoring models with a high likelihood, while penalizing those with too many endmembers. Results on real data show the interest of the proposed approach.

The intrinsic dimensionality (ID) of multivariate data is a very important concept in spectral unmixing of hyperspectral images. A good estimation of the ID is crucial for a correct retrieval of the number of endmembers (the spectral signatures of macroscopic materials) in the image, for dimensionality reduction or for subspace learning, among others. Recently, some approaches to perform spectral unmixing and superresolution locally have been proposed, which require a local estimation of the number of endmembers to use. However, the role of ID in local regions of hyperspectral images has not been properly addressed. Some important issues when dealing with small regions of hyperspectral data can seriously affect the performance of conventional hyperspectral ID estimators. We show that three factors mainly affect local ID estimation: the number of pixels in the local regions, which has to be high enough for the estimations to be relevant, the number of hyperspectral bands which complicates the estimations if the ambient space has a high dimensionality, and the noise, which can be misinterpreted as a signal when its power is important. Here, we review the hyperspectral ID estimators on the literature for local ID estimation, we show how they behave in a local setting on synthetic and real data sets, and we provide some guidelines to make proper use of these estimators in local approaches.

New hyperspectral missions will collect huge amounts of hyperspectral data. In addition, it is possible now to acquire time series and multiangular hyperspectral images. The process and analysis of these big data collections will require common hyperspectral techniques to be adapted or reformulated. The tensor decomposition, which is also known as multiway analysis, is a technique to decompose multiway arrays, i.e., hypermatrices with more than two dimensions (ways). Hyperspectral time series and multiangular acquisitions can be represented as a three-way tensor. Here, we apply canonical polyadic (CP) tensor decomposition techniques to the blind analysis ohyperspectral big data. In order to do so, we use a novel compression-based nonnegative CP decomposition. We show that the proposed methodology can be interpreted as multilinear blind spectral unmixing, i.e., a higher order extension of the widely known spectral unmixing. In the proposed approach, the big hyperspectral tensor is decomposed in three sets of factors, which can be interpreted as spectral signatures, their spatial distribution, and temporal/angular changes. We provide experimental validation using a study case of the snow coverage of the French Alps during the snow season.

Remote sensing hyperspectral images (HSIs) are quite often low rank, in the sense that the data belong to a low dimensional subspace/manifold. This has been recently exploited for the fusion of low spatial resolution HSI with high spatial resolution multispectral images in order to obtain super-resolution HSI. Most approaches adopt an unmixing or a matrix factorization perspective. The derived methods have led to state-of-the-art results when the spectral information lies in a low-dimensional subspace/manifold. However, if the subspace/manifold dimensionality spanned by the complete data set is large, i.e., larger than the number of multispectral bands, the performance of these methods mainly decreases because the underlying sparse regression problem is severely ill-posed. In this paper, we propose a local approach to cope with this difficulty. Fundamentally, we exploit the fact that real world HSIs are locally low rank, that is, pixels acquired from a given spatial neighborhood span a very low-dimensional subspace/manifold, i.e., lower or equal than the number of multispectral bands. Thus, we propose to partition the image into patches and solve the data fusion problem independently for each patch. This way, in each patch the subspace/manifold dimensionality is low enough, such that the problem is not ill-posed anymore. We propose two alternative approaches to define the hyperspectral super-resolution through local dictionary learning using endmember induction algorithms. We also explore two alternatives to define the local regions, using sliding windows and binary partition trees. The effectiveness of the proposed approaches is illustrated with synthetic and semi real data.

Spectral unmixing is a popular technique for analyzing remotely sensed hyperspectral data sets with subpixel precision. Over the last few years, many algorithms have been developed for each of the main processing steps involved in spectral unmixing (SU) under the LMM assumption: 1) estimation of the number of endmembers; 2) identification of the spectral signatures of the endmembers; and 3) estimation of the abundance of endmembers in the scene. Although this general processing chain has proven to be effective for unmixing certain types of hyperspectral images, it also has some drawbacks. The first one comes from the fact that the output of each stage is the input of the following one, which favors the propagation of errors within the unmixing chain. A second problem is the huge variability of the results obtained when estimating the number of endmembers of a hyperspectral scene with different state-of-the-art algorithms, which influences the rest of the process. A third issue is the computational complexity of the whole process. To address the aforementioned issues, this paper develops a novel negative abundance-oriented SU algorithm that covers, for the first time in the literature, the main steps involved in traditional hyperspectral unmixing chains. The proposed algorithm can also be easily adapted to a scenario in which the number of endmembers is known in advance and two additional variations of the algorithm are provided to deal with high-noise scenarios and to significantly reduce its execution time, respectively. Our experimental results, conducted using both synthetic and real hyperspectral scenes, indicate that the presented method is highly competitive (in terms of both unmixing accuracy and computational performance) with regard to other SU techniques with similar requirements, while providing a fully self-contained unmixing chain without the need for any input parameters.

The Reed-Xiaoli (RX) is considered as the benchmark algorithm in multidimensional anomaly detection (AD). However, the RX detector performance decreases when the statistical parameters estimation is poor. This could happen when the background is non-homogeneous or the noise independence assumption is not fulfilled. For a better performance, the statistical parameters are estimated locally using a sliding window approach. In this approach, called adaptive RX, a window is centered over the pixel under the test (PUT), so the background mean and covariance statistics are estimated using the data samples lying inside the window's spatial support, named the secondary data. Sometimes, a smaller guard window prevents those pixels close to the PUT to be used, in order to avoid the presence of outliers in the statistical estimation. The size of the window is chosen large enough to ensure the invertibility of the covariance matrix and small enough to justify both spatial and spectral homogeneity. We present here an alternative methodology to select the secondary data for a PUT by means of a binary partition tree (BPT) representation of the image. We test the proposed BPT-based adaptive hyperspectral RX AD algorithm using a real dataset provided by the Target Detection Blind Test project.

Remote sensing hyperspectral images (HSI) are quite often locally low rank, in the sense that the spectral vectors acquired from a given spatial neighborhood belong to a low dimensional subspace/manifold. This has been recently exploited for the fusion of low spatial resolution HSI with high spatial resolution multispectral images (MSI) in order to obtain super-resolution HSI. Most approaches adopt an unmixing or a matrix factorization perspective. The derived methods have led to state-of-the-art results when the spectral information lies in a low dimensional subspace/manifold. However, if the subspace/manifold dimensionality spanned by the complete data set is large, the performance of these methods decrease mainly because the underlying sparse regression is severely ill-posed. In this paper, we propose a local approach to cope with this difficulty. Fundamentally, we exploit the fact that real world HSI are locally low rank, to partition the image into patches and solve the data fusion problem independently for each patch. This way, in each patch the subspace/manifold dimensionality is low enough to obtain useful super-resolution. We explore two alternatives to define the local regions, using sliding windows and binary partition trees. The effectiveness of the proposed approach is illustrated with synthetic and semi-real data.

Anomaly Detection methods are used when there is not enough information about the target to detect. These methods search for pixels in the image with spectral characteristics that differ from the background. The most widespread detection test, the RX-detector, is based on the Mahalanobis distance and on the background statistical characterization through the mean vector and the covariance matrix. Although non-Gaussian distributions have already been introduced for background modeling in Hyperspectral Imaging, the parameters estimation is still performed using the Maximum Likelihood Estimates for Gaussian distribution. This paper describes robust estimation procedures more suitable for non-Gaussian environment. Therefore, they can be used as plug-in estimators for the RX-detector leading to some great improvement in the detection process. This theoretical improvement has been evidenced over two real hyperspectral images.

The snow coverage area (SCA) is one of the most important parameters for cryospheric studies. The use of remote sensing imagery can complement field measurements by providing means to derive SCA with a high temporal frequency and covering large areas. Images acquired by the Moderate Resolution Imaging Spectroradiometer (MODIS) are perhaps the most widely used data to retrieve SCA maps. Some MODIS derived algorithms are available for subpixel SCA estimation, as MODSCAG and MODImLab. Both algorithms make use of spectral unmixing techniques using a fixed set of snow, rocks and other materials spectra (endmembers). We aim to improve the performance of a modified version of MODIm-Lab algorithm by exploring advanced spectral unmixing techniques. Furthermore, we make use of endmember induction algorithms to obtain the endmembers from the data itself instead of using a fixed spectral library. We validate the proposed approach on a case study in the mountainous region of the Alps.

The binary partition tree (BPT) is a hierarchical region-based representation of an image in a tree structure. The BPT allows users to explore the image at different segmentation scales. Often, the tree is pruned to get a more compact representation and so the remaining nodes conform an optimal partition for some given task. Here, we propose a novel BPT construction approach and pruning strategy for hyperspectral images based on spectral unmixing concepts. Linear spectral unmixing consists of finding the spectral signatures of the materials present in the image (endmembers) and their fractional abundances within each pixel. The proposed methodology exploits the local unmixing of the regions to find the partition achieving a global minimum reconstruction error. Results are presented on real hyperspectral data sets with different contexts and resolutions.

This work presents a novel spatio-temporal cellular automata-based filtering (STCAF) for image sequence denoising. Most of the methods using cellular automata (CA) for image denoising involve the manual design of the rules that define the behaviour of the automata. This is a complex and not straightforward operation. In order to tackle this problem, this paper proposes to use evolutionary methods to obtain the CA set of rules which produces the best possible denoising under different noise models or/and image sources. This is implemented using a spatio-temporal neighbourhood for each pixel, which significantly improves the results with respect to simple spatio or temporal set of neighbours. The proposed method is tested to reduce the noise in low-dose X-ray image sequences. These data have a severe signal-dependent noise that must be reduced avoiding artifacts while preserving structures of interest for a medical inspection. The proposed method outperforms several state-of-the-art algorithms on both simulated and real sequences.

The Binary Partition Tree (BPT) is a hierarchical region-based representation of an image in a tree structure. BPT allows users to explore the image at different segmentation scales, from fine partitions close to the leaves to coarser partitions close to the root. Often, the tree is pruned so the leaves of the resulting pruned tree conform an optimal partition given some optimality criterion. Here, we propose a novel BPT construction approach and pruning strategy for hyperspectral images based on spectral unmixing concepts. The proposed methodology exploits the local unmixing of the regions to find the partition achieving a global minimum reconstruction error. We successfully tested the proposed approach on the well-known Cuprite hyperspectral image collected by NASA Jet Propulsion Laboratory's Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). This scene is considered as a standard benchmark to validate spectral unmixing algorithms.

Recently, a general approach for high-resolution polarimetric SAR (POLSAR) data classification in heterogeneous clutter was presented, based on a statistical test of equality of covariance matrices. Here, we extend that approach by taking advantage of the Constant False Alarm Ratio (CFAR) property of the statistical test in order to improve the clustering process. We show that the CFAR property can be used in the hierarchical segmentation of the POLSAR data images to automatically detect the number of clusters. The proposed method will be applied on a high-resolution polarimetric data set acquired by the ONERA RAMSES system.

Remote sensors capture large scenes that are conventionally split in smaller patches before being stored and analyzed. Traditionally, this has been done by dividing the scene in rectangular windows. Such windowing methodology could provoke the separation of spectrally homogeneous areas or objects of interest into two or more patches. This is due to the presence of objects of interest in correspondence to windows' borders, or because the fixed size of the windows does not adapt well to the scale of the objects. To alleviate this issue, the windows can be arranged in an overlapping way, incurring in some data redundancy storage. Recently, tree representations have been used as an alternative to windowing in order to structure and store large amounts of remote sensing data. In this work we explore the benefits of using Binary Partition Trees (BPT) instead of windowing to store hyperspectral large scenes. We are particularly interested in storing the information resulting of local spectral unmixing processes running over a large real hyperspectral scene. We show that under similar conditions BPT allows a better storage of the unmixing information in terms of reconstruction error.

Mathematical morphology is the non-linear Lattice Theory based construction of image filters. However, multivariate images, such as hyperspectral images, don’t have a total order and existing methods don’t fully exploit the spectral information. Recently supervised orderings were proposed for the definition of a total order in hyperspectral data. In a recent work we proposed the use of Lattice Associative Memories (LAAMs) to build up a supervised ordering. Here we follow that avenue and introduce an absolute LAAM supervised ordering. Supervised ordering rely on the definition of a foreground and background sets of training data points. We propose an automatic methodology to construct the training sets without a-priori information. For that, we make use of endmember induction algorithms. We demonstrate some results on the well known Pavia image.