Hyperspectral change detection (HCD) has found numerous key applications, such as land cover monitoring. The majority of benchmark HCD algorithms are semi-supervised methods, and some of them can even achieve very low sample labeling rates. However, in some practical scenarios, such as those requiring immediate detection responses for onboard edge computing, we need to achieve the zero-label requirement as ground-truth labeling would not be available onboard for newly acquired images. In this work, we propose a fully unsupervised HCD algorithm, together with a lightweight model, quite suitable for onboard detection missions. Based on an iteratively augmented training set that safely collects some unchanged pixel samples, we learn an iteratively refined spectrum calibration function that eventually compensates the variability of acquisition conditions (often observed in bitemporal images), thereby making the changed pixels easily detectable by analyzing the calibrated spectra. The proposed hyperspectral looping unsupervised calibration and incremental detection (HyperLUCID) algorithm is not only computationally efficient (around 1 to 2 orders of magnitude faster than most benchmark HCD methods), but has also achieved state-of-the-art results (around 93.6% to 97.9% overall accuracy) on several real benchmark HCD datasets. Source codes: https://github.com/IHCLab/HyperLUCID.

As most optical satellites remotely acquire multispectral images (MSIs) with limited spatial resolution, multispectral unmixing (MU) becomes a critical signal processing technology for analyzing the pure material spectra for high-precision classification and identification. Unlike the widely investigated hyperspectral unmixing (HU) problem, MU is much more challenging as it corresponds to the underdetermined blind source separation (BSS) problem, where the number of sources is larger than the number of available multispectral bands. In this article, we transform MU into its overdetermined counterpart (i.e., HU) by inventing a radically new quantum deep image prior (QDIP), which relies on the virtual band-splitting task conducted on the observed MSI for generating the virtual hyperspectral image (HSI). Then, we perform HU on the virtual HSI to obtain the virtual hyperspectral sources. Though HU is overdetermined, it still suffers from the ill-posed issue, for which we employ the convex geometry structure of the HSI pixels to customize a weighted simplex shrinkage (WSS) regularizer to mitigate the ill-posedness. Finally, the virtual hyperspectral sources are spectrally downsampled to obtain the desired multispectral sources. The proposed geometry/quantum-empowered MU (GQ- $\mu $ ) algorithm can also effectively obtain the spatial abundance distribution map for each source, where the geometric WSS regularization is adaptively and automatically controlled based on the sparsity pattern of the abundance tensor. Simulation and real-world data experiments demonstrate the practicality of our unsupervised GQ- $\mu $ algorithm for the challenging MU task. Ablation study demonstrates the strength of QDIP, not achieved by classical DIP, and validates the mechanics-inspired WSS geometry regularizer. The associated code will be available at https://github.com/IHCLab/GQ-mu.

The Sentinel-2 satellite, launched by the European Space Agency (ESA), offers extensive spatial coverage and has become indispensable in a wide range of remote sensing applications. However, it just has 12 spectral bands, making substances/objects identification less effective, not mentioning the varying spatial resolutions (10/20/60 m) across the 12 bands. If such a multi-resolution 12-band image can be computationally converted into a hyperspectral image with uniformly high resolution (i.e., 10 m), it significantly facilitates remote identification tasks. Though there are some spectral super-resolution methods, they did not address the multi-resolution issue on one hand, and, more seriously, they mostly focused on the CAVE-level hyperspectral image reconstruction (involving only 31 visible bands) on the other hand, greatly limiting their applicability in real-world remote sensing scenarios. We ambitiously aim to convert Sentinel-2 data directly into NASA’s AVIRIS-level hyperspectral image (encompassing up to 172 visible and near-infrared (NIR) bands, after ignoring those absorption/corruption ones). For the first time, this paper solves this specific super-resolution problem (highly ill-posed), allowing all historical Sentinel-2 data to have their corresponding high-standard AVIRIS counterparts. We achieve so by customizing a novel algorithm that introduces deep unfolding regularization andQ-quadratic-norm regularization into the so-called convex/deep (CODE) small-data learning criterion. Based on the derived spectral-spatial duality, the proposed interpretable COS2A algorithm demonstrates superior spectral super-resolution results across diverse land cover types, as validated through extensive experiments. Source codes: https://github.com/IHCLab/COS2A.

Multispectral unmixing (MU) is critical due to the inevitable mixed-pixel phenomenon caused by the limited spatial resolution of typical multispectral images (MSIs) in remote sensing. However, MU mathematically corresponds to the underdetermined unsupervised source separation (USS) problem, thus highly challenging, making it a daunting task for researchers to tackle it. Previous MU works all ignore the underdetermined issue and merely consider scenarios with more bands than sources. This work attempts to resolve the underdetermined issue by further conducting the light-splitting task using a network-inspired virtual prism, and as this task is challenging, we achieve so by incorporating very advanced quantum feature extraction techniques. We emphasize that the prism is virtual (allowing us to fix the spectral response as a simple deterministic matrix), so the virtual hyperspectral image (HSI) it generates does not need to correspond to some real hyperspectral sensor; in other words, it is good enough as long as the virtual HSI satisfies some fundamental properties of light splitting (e.g., nonnegativity and continuity). With the above virtual quantum prism, we know that the virtual HSI is expected to possess some desired simplex structure. This allows us to adopt the convex geometry (CG) to unmix the spectra, followed by downsampling the pure spectra back to the multispectral domain, thereby achieving MU. Experimental evidence shows the great potential of our MU algorithm, termed prism-inspired multispectral endmember extraction (PRIME).

Inland waterbody detection (IWD), which aims at identifying and mapping waterbodies such as rivers, lakes, and reservoirs, is critical for water resources management and agricultural planning. However, the development of high-fidelity IWD mapping technology remains unresolved. We aim to propose a practical solution using only the easily accessible delay-Doppler map (DDM) data provided by NASA’s Cyclone Global Navigation Satellite System (CYGNSS), which facilitates effective estimation of physical parameters on the Earth’s surface with high temporal resolution and wide spatial coverage. Specifically, as quantum deep network (QUEEN) has revealed its strong proficiency in addressing classification-like tasks, we encode the DDM using a customized transformer, followed by feeding the transformer-encoded DDM (tDDM) into a highly entangled QUEEN to distinguish whether the tDDM corresponds to a hydrological region. In recent literature, QUEEN has achieved outstanding performances in numerous challenging remote sensing tasks (e.g., hyperspectral restoration, change detection, and mixed noise removal, etc.), and its high effectiveness stems from the fundamentally different way it adopts to extract features (the so-called quantum unitary-computing features). The meticulously designed IWD-QUEEN retrieves high-precision river textures, such as those in Amazon River Basin in South America, demonstrating its superiority over traditional classification methods and existing global hydrography maps. IWD-QUEEN, together with its parallel quantum multihead scheme, works in a near-real-time manner (i.e., millisecond-level computing per DDM data). To broaden accessibility for users of traditional computers, we also provide the non-quantum counterpart of our method, called IWD-Transformer, thereby increasing the impact of this work. In terms of quantitative evaluation, IWD-QUEEN leads the IWD-Transformer by approximately 7% and 8% in F1-score and Cohen’s kappa, respectively, alluding the promising role of QUEEN in achieving high-performance detection. Source codes: https://github.com/IHCLab/IWD-QUEEN.

A mangrove mapping (MM) algorithm is an essential classification tool for environmental monitoring. The recent literature shows that compared with other index-based MM methods that treat pixels as spatially independent, convolutional neural networks (CNNs) are crucial for leveraging spatial continuity information, leading to improved classification performance. In this work, we go a step further to show that quantum features provide radically new information for CNN to further upgrade the classification results. Simply speaking, CNN computes affine-mapping features, while quantum neural network (QNN) offers unitary-computing features, thereby offering a fresh perspective in the final decision-making (classification). To address the challenging MM problem, we design an entangled spatial-spectral quantum feature extraction module. Notably, to ensure that the quantum features contribute genuinely novel information (unaffected by traditional CNN features), we design a separate network track consisting solely of quantum neurons with built-in interpretability. The extracted pure quantum information is then fused with traditional feature information to jointly make the final decision. The proposed quantum-empowered deep network (QEDNet) is very lightweight, so the improvement does come from the cooperation between CNN and QNN (rather than parameter augmentation). Extensive experiments will be conducted to demonstrate the superiority of QEDNet.

Quantum machine intelligence starts showing its impact on satellite remote sensing (SRS). Also, recent literature exhibits that quantum generative intelligences encompass superior potential than their classical counterpart, motivating us to develop quantum generative adversarial networks (GANs) for SRS. However, existing quantum GANs are restricted by the limited quantum bit (qubit) resources of current quantum computers and process merely a small 2 × 2 grayscale image, far from being applicable to SRS. Recently, the novel concept of hybrid quantum-classical GAN, a quantum generator with a classical discriminator, has upgraded the order to 28 × 28 (still grayscale), whereas it is still insufficient for SRS. This motivates us to design a radically new hybrid framework, where both generator and discriminator are hybrid architectures. We demonstrate this feasibility, leading to a breakthrough of processing 128×128 hyperspectral images for SRS. Specifically, we design the quantum part with mathematically provable quantum full expressibility (FE) to address core signal processing tasks, wherein the FE property allows the quantum network to realize any valid quantum operator with appropriate training. The classical part, composed of convolutional layers, treats the read-in (compressing the optical information into limited qubits) and read-out (addressing the quantum collapse effect) procedures. The proposed innovative hybrid quantum GAN, named “Hyperspectral Knot-like IntelligeNt dIscrimiNator and Generator” (HyperKING), where “knot” partly symbolizes the quantum entanglement and partly the compressed quantum domain in the central part of the network architecture. HyperKING significantly surpasses the classical approaches in hyperspectral tensor completion, mixed noise removal (about 3dB improvement), and blind source separation results.

Due to the intensifying impacts of extreme climate changes, drought forecasting (DF), which aims to predict droughts from historical meteorological data, has become increasingly critical for monitoring and managing water resources. Despite the spatial coherence of drought conditions, benchmark deep learning-based DF models predict each region independently while ignoring the neighboring spatial information. Using the Standardized Precipitation Evapotranspiration Index (SPEI), we designed and trained a novel and transformative spatially-aware DF neural network, which effectively captures local interactions among neighboring regions, resulting in enhanced spatial coherence and prediction accuracy. As DF also requires sophisticated temporal analysis, the Mamba network, recognized as the most accurate and efficient existing time-sequence modeling, was adopted to extract temporal features from short-term time frames. We also adopted quantum neural networks (QNN) to entangle the spatial features of different time instances, leading to refined spatiotemporal features of seven different meteorological variables for effectively identifying short-term climate fluctuations. In the last stage of our proposed SPEI-driven quantum spatially-aware Mamba network (SQUARE-Mamba), the extracted spatiotemporal features of seven different meteorological variables were fused to achieve more accurate DF. Validation experiments across El Niño, La Niña, and normal years demonstrated the superiority of the proposed SQUARE-Mamba, remarkably achieving an average improvement of more than 9.8% in the coefficient of determination index (R2) compared to baseline methods, thereby illustrating the promising roles of the temporal quantum entanglement and Mamba temporal analysis to achieve more accurate DF. Notably, the integration of QNN further upgrades the naive Mamba baseline by over 2.7% in R2on average, highlighting the model’s sensitivity to transient climate variations.

Hyperspectral anomaly detection (HAD), a challenging inverse problem, has found numerous scientific applications. Although extant HAD algorithms have achieved remarkable results, there are still several issues remained unresolved: 1) low spatial resolution (and spectral redundancy) in typical hyperspectral images prevents effectively distinguishing the abnormal pixels from those normal ones and 2) the reconstruction from existing residual-based frameworks would not completely remove anomaly effects, making the detection solely from the residual impractical. In this article, we propose a novel HAD method, termed transformer-guided fractional attention within the abundance domain (TGFA-AD), which substitutes raw input image with the abundance matrix obtained via blind source separation (BSS). First, the proposed abundance spatial-channel reconstruction transformer (ASCR-Former) is customized for rebuilding the abundance matrix. According to the image self-similarity, the abundance is patch-wisely encoded with class (CLS) tokens. The transformer encoders intensify the spatial and channel characteristics between tokens for reconstructing the abundance, followed by deriving the initial detection from the abundance residual matrix. Second, a novel fractional abundance attention (FAA) mechanism is proposed, where the attention weights coming from a specific linear combination of abundances are guided by the initial detection with convex $ Q$ -quadratic norm. Finally, the fractional convolution is incorporated to fuse the abundance and residual into the fractional feature for yielding the final detection result. Real data experiments quantitatively and qualitatively exhibit the state-of-the-art performance of TGFA-AD.

Adversarial learning is of paramount importance in numerous recent computing areas, while quantum entanglement has also revealed its role in efficient computing. This motivated us to bring quantum computing into adversarial learning. Though there are some preliminary theoretical studies of quantum adversarial learning (QAL), there has no demonstration of advanced real-world applications. For the first time, we design and implement a QAL framework, and demonstrate the feasibility of QAL-based hyperspectral image processing for remote sensing. This research line aims to lay the foundation for the QAL in hyperspectral remote sensing, including to solve the limited qubit resources, to mitigate the quantum collapse effect, to design a quantum discriminator with comparable ability, as well as to ensure the quantum expressibility of the generator, to name a few.

Synthesis of high-resolution (HR) FORMOSAT-8 satellite image is a critical task with high economical values, not only for avoiding related issues before launching FORMOSAT-8, but also for predicting and understanding the potential applications like precision agriculture. Nevertheless, there is no existing techniques for this mission, motivating us to reconsider the synthesis problem as a super-resolution problem under the satellite image fusion framework. Specifically, we employ the Sentinel-2 and Pléiades satellite images based on their fundamental properties (e.g., band alignment, and spatial resolution), and trickily fuse them to generate the target image (i.e, the HR FORMOSAT-8 image). Our fusion algorithm adopts the convex/deep (CODE) small-data learning theory, recently invented in the remote sensing area, resulting in a fast (closed-form) and high-quality synthesis 4m product.

Super-resolving remotely acquired hyperspectral images, often with low resolution (LR), is a critical signal processing technique, as it greatly affects the subsequent material classification and identification tasks. An economical approach in the remote sensing area is to fuse the spatial details extracted from the high-resolution (HR) counterpart multispectral image into the LR hyperspectral image, thereby inferring the desired HR hyperspectral image. Convex analysis has been shown to be an effective tool for the fusion mission, but it often relies on sophisticated regularization schemes to tackle this challenging inverse problem. In the existing literature, the deep plug-and-play strategy was proposed for fast implementation of those sophisticated regularizers, but just approximately without convergence guarantees. Thus, we introduce deep learning (in an alternative approach) to tailor a simple convex regularizer for efficient super-resolution. Remarkably, though typical deep fusion methods can tackle non-linear effect presented in real hyperspectral data, they often rely on big data and sophisticated network structures, which are often time-consuming and resource-intensive. Instead, our deep regularizer just needs a small-data-driven simple network architecture that implies better stability and tractability; we achieve so by reconsidering the role of deep learning as simply to guide the convex algorithm to search the fusion solution, rather than directly serving as the final solution. The proposed convex deep image fusion (CODE-IF) algorithm, with all the closed-form algorithmic expressions derived, achieves state-of-the-art hyperspectral super-resolution performance.

Considering that hyperspectral image (HSI) is often of lower spatial resolution when compared to multispectral image (MSI), an economical approach for obtaining a high-spatial-resolution (HSR) HSI is to fuse the acquired HSI and MSI, thereby greatly facilitating the subsequent material identification and classification in satellite remote sensing. As satellite-acquired HSI and MSI are often misaligned, the proposed deep neural network does not require the input HSI/MSI to be spatially co-registered, making the challenging fusion network design even more difficult. In this study, we propose a streamlined and efficient convex model integrated into the sub-network, which obviates the need for complex network structures in learning spatial-spectral relationships, effectively guiding the quasi-residual learning task in our alignment-free fusion network. The convex sub-network is a low-rank model that leverages the convex geometric structure implicitly embedded in the hyperspectral signature space. To address the misalignment between HSI and MSI effectively, we introduce a novel Shifted Window Attention Module (SWAM) that exploits the neighboring correlation in the feature domain, significantly enhancing the performance and stability of the fusion task. Capitalizing on the redundancy among spectrums, we employ grouped convolution to decrease the computational complexity without causing additional performance degradation. The proposed Quasi-residual Convex Deep Network (QRCODE) demonstrates state-of-the-art performance in alignment-free HSI/MSI fusion tasks.

Recently, numerous hyperspectral anomaly detection (HAD) methods have been proposed for broad and crucial applications. Among these, robust principal component analysis (RPCA) gains considerable attention in HAD, as it separates the matrix into global low-rank (LR) and sparse components, corresponding to the property of background and anomaly. However, RPCA solves the problem by treating hyperspectral imagery (HSI) as a matrix, but this approach alone cannot well-describe the local spatial texture information. In addition, a pixelwise detection method, collaborative representation detector (CRD), has been proposed, which exploits the vital piece of local information by assuming that background pixels can be composed of their neighbor pixels, while abnormal ones cannot. Although several CRD-based methods achieve promising HAD performances, they generally suffer from high computational costs due to the pixelwise optimization scheme. To overcome the aforementioned two limitations, we propose a novel algorithm, SuperRPCA. First, we improve CRD to superpixelwise calculation and reconstruct the background with a simplex-based algebraic solution. Subsequently, the rebuilt background is tailored to serve as a convex regularizer and integrated into RPCA. Besides, the regularizer inherently possesses an LR property, adeptly substituting the nuclear norm in traditional RPCA and hence significantly reducing computational costs. SuperRPCA demonstrates easily identifiable visual qualities and state-of-the-art quantitative performance with all the closed-form algorithmic expressions explicitly derived.

Change detection (CD) is a critical remote sensing technique for identifying changes in the Earth’s surface over time. The outstanding substance identifiability of hyperspectral images (HSIs) has significantly enhanced the detection accuracy, making hyperspectral CD (HCD) an essential technology. The detection accuracy can be further upgraded by leveraging the graph structure of HSIs, motivating us to adopt the graph neural networks (GNNs) in solving HCD. For the first time, this work introduces a quantum deep network (QUEEN) into HCD. Unlike GNN and CNN, both extracting the affine-computing features, QUEEN provides fundamentally different unitary-computing features. We demonstrate that through the unitary feature extraction procedure, QUEEN provides radically new information for deciding whether there is a change or not. Hierarchically, a graph feature learning (GFL) module exploits the graph structure of the bitemporal HSIs at the superpixel level, while a quantum feature learning (QFL) module learns the quantum features at the pixel level, as a complementary to GFL by preserving pixel-level detailed spatial information not retained in the superpixels. In the final classification stage, a quantum classifier is designed to cooperate with a traditional fully connected classifier. The superior HCD performance of the proposed QUEEN-empowered GNN (i.e., QUEEN-$\mathcal {G}$) will be experimentally demonstrated on real hyperspectral datasets.

In hyperspectral remote sensing (HRS), signal sub-space identification is a critical step in many widely renowned HRS algorithms, while the accuracy of the subspace identification relies on the complete information of the data pixels. However, as the sensor arrays would be partially damaged after the satellites are launched, hyperspectral pixels are quite often incompletely acquired. Even for those renowned algorithms, they simply remove those incomplete pixels when computing the hyperspectral signal subspace. Nevertheless, even if some spectral bands of a given incomplete pixel are missing, we intuitively believe that the remaining bands of that pixel should still contribute to the accuracy of the subspace identification. We design a computationally efficient algorithm, termed as subspace identification for incomplete signals of hyperspectral image (SISHY), to utilize the information embedded in those incomplete pixels. To this end, we prove a lemma that allows us to reformulate the algebraic identification problem into an affine geometry problem, thereby allowing us to flexibly add suitable regularizer for better identification result as needed. SISHY judiciously associates the regularized subspace identification problem with a denoising operator, thereby allowing an efficient algorithm implementation and yielding a physically interpretable data matrix completion result as a byproduct. Experiments demonstrate that the SISHY algorithm does improve the efficacy of the subsequent tasks of unmixing, inpainting and classification.

Hyperspectral dehazing (HyDHZ) has become a crucial signal processing technology to facilitate the subsequent identification and classification tasks, as the airborne visible/infrared imaging spectrometer (AVIRIS) data portal reports a massive portion of haze-corrupted areas in typical hyperspectral remote sensing images. The idea of inverse problem transform (IPT) has been proposed in recent remote sensing literature in order to reformulate a hardly tractable inverse problem (e.g., HyDHZ) into a relatively simple one. Considering the emerging spectral super-resolution (SSR) technique, which spectrally upsamples multispectral data to hyperspectral data, we aim to solve the challenging HyDHZ problem by reformulating it as an SSR problem. Roughly speaking, the proposed algorithm first automatically selects some uncorrupted/informative spectral bands, from which SSR is applied to spectrally upsample the selected bands in the feature space, thereby obtaining a clean hyperspectral image (HSI). The clean HSI is then further refined by a deep transformer network to obtain the final dehazed HSI, where a global attention mechanism is designed to capture nonlocal information. There are very few HyDHZ works in existing literature, and this article introduces the powerful spatial–spectral transformer into HyDHZ for the first time. Remarkably, the proposed transformer-driven IPT-based HyDHZ (T2HyDHZ) is a blind algorithm without requiring the user to manually select the corrupted region. Extensive experiments demonstrate the superiority of T2HyDHZ with less color distortion.

Hyperspectral tensor completion (HTC) for remote sensing, critical for advancing space exploration and other satellite imaging technologies, has drawn considerable attention from recent machine learning community. Hyperspectral image (HSI) contains a wide range of narrowly spaced spectral bands hence forming unique electrical magnetic signatures for distinct materials, and thus plays an irreplaceable role in remote material identification. Nevertheless, remotely acquired HSIs are of low data purity and quite often incompletely observed or corrupted during transmission. Therefore, completing the 3-D hyperspectral tensor, involving two spatial dimensions and one spectral dimension, is a crucial signal processing task for facilitating the subsequent applications. Benchmark HTC methods rely on either supervised learning or nonconvex optimization. As reported in recent machine learning literature, John ellipsoid (JE) in functional analysis is a fundamental topology for effective hyperspectral analysis. We therefore attempt to adopt this key topology in this work, but this induces a dilemma that the computation of JE requires the complete information of the entire HSI tensor that is, however, unavailable under the HTC problem setting. We resolve the dilemma, decouple HTC into convex subproblems ensuring computational efficiency, and show state-of-the-art HTC performances of our algorithm. We also demonstrate that our method has improved the subsequent land cover classification accuracy on the recovered hyperspectral tensor.

Considering that there are many NP-hard problems in remote sensing (e.g., Craig simplex computation in hyperspectral un-mixing), it is natural to introduce quantum computing into space remote sensing. However, current quantum computers have some practical limitations, requiring complementary techniques to support quantum computing. Specifically, we are introducing artificial intelligence (AI) to solve the quantum collapse effect and the phenomenon of insufficient quantum bits (qubits). We thereby propose the hyperspectral quantum deep network (HyperQUEEN) for satellite remote sensing. HyperQUEEN is the first quantum technology that successfully outputs a complete hyperspectral image, given the very limited qubit resources. Existing quantum image processing methods can only achieve classification-level tasks or simple geometry transforms, and are far from being applicable to advanced satellite missions like restoration of damaged hyperspectral images, which HyperQUEEN has successfully achieved for the first time. Remarkable computational efficiency and restoration performances achieved by the radically new quantum AI system—HyperQUEEN—will be reported.

Quantum science just winning the 2022 Nobel Prize in Physics must lead future development of remote sensing technologies. However, given the very limited number of entangled quantum bits (qubits) even in the most advanced quantum computers, is processing remotely sensed hyperspectral image (featured by its large data volume) using quantum computer technically feasible? Even if the quantum image state can be well processed to the quantum state of the target image (QSTI), it cannot be perfectly retrieved/output as the QSTI will collapse to some eigenstate once it is measured. Owing to these challenges, current quantum image processing technologies can only achieve classification-level applications requiring just a few output qubits. We design a hyperspectral quantum deep network (HyperQUEEN) to encode the hyperspectral information using very few qubits, as well as to learn the mapping from some measuring statistics (associated with the collapsed-QSTI) to the target image (instead of directly retrieving the unobservable QSTI), thereby solving the challenges. HyperQUEEN is the first quantum architecture that makes a breakthrough to blindly reconstruct NASA’s damaged hyperspectral images, which means a lot for the upcoming space era. As the immature quantum facility nowadays does not yet allow us to fully exhibit its high potential, we are not aiming at developing state-of-the-art methods, but are demonstrating the feasibility of quantum hyperspectral remote sensing. Mathematical analysis guiding our design toward the low-rank quantum deep network, together with comprehensive experiments, will also be reported.

Mangrove mapping (MM) is a critical satellite remote sensing technology since mangrove forests have a large capacity for carbon storage among the blue carbon ecosystems. However, we surprisingly found that benchmark MM methods are all index-based ones, completely ignoring the spatially neighboring information on the one hand and quite sensitive to the threshold setting on the other hand. Deep learning has been proven to be an effective solution for incorporating the desired spatial information, but the induced big data collection of MM is difficult and time-consuming, especially for ground-truth labeling; this would be the reason why benchmark methods are all index-based ones. To solve the dilemma, we introduce convex analysis into deep learning, thereby achieving small-data learning. The proposed algorithm is hence termed convex deep MM (CODE-MM), mainly developed for the Sentinel-2 satellite, which is the mainstream satellite for the MM mission, as it involves those key green/infrared bands for characterizing mangrove multispectral signatures. We also generalize our CODE-MM to test the hyperspectral satellite data, which should be the trend for various classification missions in the future due to its strong material identifiability. Simply speaking, CODE-MM first infers a rough mangrove signature for designing a Siamese deep regularizer, which is then plugged into a convex criterion customized for the mapping task. We implement the convex criterion by deriving closed-form solutions for all the algorithmic steps, ensuring computational efficiency. Extensive experiments demonstrate that CODE-MM is insensitive to the threshold setting and yields state-of-the-art performance in accurate mangrove forest mapping.

With recent advances in hyperspectral remote sensing, hyperspectral change detection (HCD) methods have been developed for precision agriculture and land cover/use monitoring. Among the hyperspectral techniques, those based on convex optimization (CO) and deep learning (DE) have gained particular attentions. However, DE often relies on a vast amount of training data (big data) and time-consuming manual labeling tasks, in order to learn the inherent patterns of hyperspectral images (HSIs). On the other hand, CO typically requires sophisticated mathematical regularization terms for effectively and adaptively addressing the ill-posed HCD inverse problem. Considering these challenges, we employ the convex deep (CODE) small-data learning theory recently invented for hyperspectral satellite remote sensing, and propose a semi-supervised graph neural network to achieve very low labeling rates. Furthermore, the proposed CODE-HCD method exploits hyperspectral data affine geometry to design a convexQ-quadratic norm regularizer, whose mathematical form is very simple and thereby ensures a computationally efficient algorithm. The superiority of CODE-HCD over benchmark methods will be demonstrated on several real-world hyperspectral datasets.

Hyperspectral anomaly detection (HAD) is a crucial task that aims to classify the given image into abnormal pixels and background pixels. Besides, the classification boundary between the abnormal pixels and the background pixels is implicit, making HAD a challenging problem. An existing method for anomaly detection is proposed based on collaborative representation. Since the method performs the detection on each pixel, it is not computationally efficient. To reduce the computational cost, we develop a new method based on collaborative representation. First, superpixel segmentation is utilized to cluster the image. Then, we perform the collaborative representation on each superpixel to obtain a rough detection result. According to the preliminary result, a threshold is automatically calculated to classify potential abnormal superpixels and background superpixels. At last, the boundaries of abnormal superpixels are refined to yield a more accurate detection result. In the real data experiments, we show that our method has satisfactory visual qualities and state-of-the-art quantitative performance.

In the remote sensing field, the spatial resolution of hyperspectral images (HSIs) is poor compared to RGB and multispectral images. Hence, hyperspectral image super-resolution (HISR) has become a popular topic recently. A branch of HISR methods is based on image fusion, but these methods rely on high-spatial-resolution counterpart image (e.g., multispectral image of the same scene) that is, however, not always available. Therefore, developing single hyperspectral image super-resolution (SHISR) method is highly desired. Due to the lack of abundant high-quality HSIs (i.e., big data) in satellite remote sensing, deep learning itself would be insufficient to well solve SHISR. We solve SHISR based on the recently invented ADMM-Adam learning theory, which blends the advantages from deep learning and convex optimization, thereby allowing software engineers to solve various challenging inverse problems without big data and sophisticated regularizer. For the first time, ADMM-Adam is adopted to solve SHISR in this paper, and experimental evidences well support its superiority even just with small data.

MOTIVATION: Complex biological tissues are often a heterogeneous mixture of several molecularly distinct cell subtypes. Both subtype compositions and subtype-specific (STS) expressions can vary across biological conditions. Computational deconvolution aims to dissect patterns of bulk tissue data into subtype compositions and STS expressions. Existing deconvolution methods can only estimate averaged STS expressions in a population, while many downstream analyses such as inferring co-expression networks in particular subtypes require subtype expression estimates in individual samples. However, individual-level deconvolution is a mathematically underdetermined problem because there are more variables than observations. RESULTS: We report a sample-wise Convex Analysis of Mixtures (swCAM) method that can estimate subtype proportions and STS expressions in individual samples from bulk tissue transcriptomes. We extend our previous CAM framework to include a new term accounting for between-sample variations and formulate swCAM as a nuclear-norm and ℓ2,1-norm regularized matrix factorization problem. We determine hyperparameter values using cross-validation with random entry exclusion and obtain a swCAM solution using an efficient alternating direction method of multipliers. Experimental results on realistic simulation data show that swCAM can accurately estimate STS expressions in individual samples and successfully extract co-expression networks in particular subtypes that are otherwise unobtainable using bulk data. In two real-world applications, swCAM analysis of bulk RNASeq data from brain tissue of cases and controls with bipolar disorder or Alzheimer's disease identified significant changes in cell proportion, expression pattern and co-expression module in patient neurons. Comparative evaluation of swCAM versus peer methods is also provided. AVAILABILITY AND IMPLEMENTATION: The R Scripts of swCAM are freely available at https://github.com/Lululuella/swCAM. A user's guide and a vignette are provided. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Coexistence and interference management issues for machine-to-machine (M2M) and human-to-human (H2H) communications are crucial for the Internet of Things (IoT). This article considers beamforming and power allocation for M2M/H2H coexistence networks adopting the dynamic time division duplex (TDD) spectrum sharing scheme and energy harvesting (EH). The design objective is total system power minimization with device Quality-of-Service (QoS) constraints as well as EH constraints. Since the dynamic TDD introduces new types of interference, i.e., uplink/downlink cross-interference, the considered problem is a challenging nonconvex coupled problem. We first consider a simplified problem without the EH considerations. We propose a novel low-complexity algorithm based on uplink-downlink duality (UDD) and alternating optimization (AO) to tackle this problem. Then, we propose a second-order cone programming (SOCP) relaxation-based AO low-complexity algorithm to deal with the general problem. In the simulation, we study the performance of the QoS, the number of antennas, the number of users, and the power splitting ratio. Finally, the performance of the proposed algorithms have low-complexity than the classical convex optimization method.

Hyperspectral compressed sensing (HCS) for the miniaturized satellite is challenging mainly due to the required lightweight onboard hardware and the necessary low sampling rate. Optical devises involved in conventional HCS include spectral splitter (SS), digital micromirror device (DMD) array, and cylindrical lens (CL), while DMD array (used for implementing random projections) is known to be bulky. We are, hence, thinking of the possibility of just using SS and CL, mathematically meaning that only the deterministic addition operator is available in the coding stage. Another recent advance in the multifunctional metamaterial also motivates us to solve such mathematical challenges. Specifically, SS and CL can be designed on a single nanoscale metasurface (flat), more in line with the miniaturized satellite application. We show that this all-addition coding scheme is achievable though it induces a far more challenging decoding stage, for which a convex decoding criterion is proposed based on self-similarity, a well-known property in imaging inverse problems. Self-similarity regularizer has recently been explicitly defined as a convex function and is demonstrated to be effective in decoding even with a low sampling rate. In addition, as the fundamental role of the John ellipsoid (JE) has been revealed in recent hyperspectral analysis literature, we build a JE-based convex analysis framework to ensure exact recovery even with low data purity. Experimental evidence shows the superiority of the proposed method.

Alternating direction method of multipliers (ADMM) and adaptive moment estimation (ADAM) are two optimizers of paramount importance in convex optimization (CO) and deep learning (DL), respectively. Numerous state-of-the-art algorithms for solving inverse problems are achieved by carefully designing a convex criterion, typically composed of a data-fitting term and a regularizer. Even when the regularizer is convex, its mathematical form is often sophisticated, hence inducing a math-heavy optimization procedure and making the algorithm design a daunting task for software engineers. Probably for this reason, people turn to solve the inverse problems via DL, but this requires big data collection, quite time-consuming if not impossible. Motivated by these facts, we propose a new framework, termed as ADMM-ADAM, for solving inverse problems. As the key contribution, even just with small/single data, the proposed ADMM-ADAM is able to exploit DL to obtain a convex regularizer of very simple math form, followed by solving the regularized criterion using simple CO algorithm. As a side contribution, a state-of-the-art hyperspectral inpainting algorithm is designed under ADMM-ADAM, demonstrating its superiority even without the aid of big data or sophisticated mathematical regularization.

Unlike RGB images available almost everywhere, hyperspectral remote sensing images are not easily obtainable, making big data collection often infeasible for a target task. This would prevent the adoption of the powerful deep learning technology from being applied in solving some challenging problems, e.g., recovering the missing part of a hyperspectral data cube (viewed as a 3-way tensor). This fact induces a series of research works to investigate how to augment the small data, for example, by rotation. We just accept the fact that only small data is available, and propose a radically different view (without augmentation) to address the lacking of big data in hyperspectral remote sensing. Specifically, we show that a deep neural network trained using just small data can still output some useful information to be used in designing regularizer for the ill-posed hyperspectral tensor completion (HTC) problem. Such regularizer is made simple and convex, thereby allowing us to design a fast convex optimization based HTC algorithm, whose superiority is experimentally demonstrated.

Acquiring high-spatial-resolution (HSR) images at high temporal sampling rate is not economical and even not achievable using contemporary multispectral satellite imaging hardware. An alternative is to fuse a set of HSR images acquired at low sampling rate, with another set of low-spatial-resolution images acquired at high sampling rate, and such fusion problem is referred to as spatiotemporal super-resolution (STSR). We mitigate the ill-posedness of the STSR problem by incorporating the image self-similarity prior (S2P), which is the key behind the design of several state-of-the-art imaging inverse problems. Unlike most super-resolution works in the computer vision area, our method does not rely on collecting big data. Instead, we propose a fully unsupervised STSR method by adopting the popular strategy in machine learning, known as plug-and-play optimization, and by carefully refining the required matrix computation/inversion. We term our method as STSRS2P, whose superiority and low computational complexity will be experimentally verified.

Requirements of compressed sensing techniques targeted at miniaturized hyperspectral satellite applications include lightweight onboard hardware, high-speed sensing, low sampling rate for compressing the massive volume of typical hyperspectral data, and noise robustness for reliable data transmission to the ground station. We achieve all these aims via deep learning, and neural networks resulted from which can be implemented on-chip, thereby allowing light hardware implementation. Our neural networks were trained from small-scaled data, but, even so, the resulting encoder achieves a very low sampling rate and very high speed. Unlike typical network training, the input-output pairs are not square but stripe-like images, partly because compressed acquisition does not allow performing compression after obtaining complete data cube and partly because stripe-like acquisition well matches the popular pushbroom hyperspectral sensing schemes. Even with such hard restriction caused by nontraditional training, the resulting decoder still reconstructs the image with high accuracy. To match the requirement of pushbroom sensing, a lightweight encoder is proposed to compress the stripe-like images immediately. Meanwhile, multiscale feature fusion block (MFB) and aggregation (MFA) modules are proposed to form our decoder for enhancing the feature representation of the compressed acquisitions. Furthermore, we achieve joint spatial/spectral super-resolution (SR) progressively, ensuring accurate hyperspectral reconstruction via a low-rank-driven decoder. The encoder and decoder are trained in an end-to-end manner, where noise robustness is forced during the training stage. Comprehensive experiments demonstrate the superiority of the proposed hyperspectral compressed sensing method, as well as its one-shot transfer learning (OTL)-based extension, both quantitatively and qualitatively.

Nonnegative blind source separation (nBSS) is often a challenging inverse problem, namely, when the mixing system is ill-conditioned. In this work, we focus on an important nBSS instance, known as hyperspectral unmixing (HU) in remote sensing. HU is a matrix factorization problem aimed at factoring the so-called endmember matrix, holding the material hyperspectral signatures, and the abundance matrix, holding the material fractions at each image pixel. The hyperspectral signatures are usually highly correlated, leading to a fast decay of the singular values (and, hence, high condition number) of the endmember matrix, so HU often introduces an ill-conditioned nBSS scenario. We introduce a new theoretical framework to attack such tough scenarios via the John ellipsoid (JE) in functional analysis. The idea is to identify the maximum volume ellipsoid inscribed in the data convex hull, followed by affinely mapping such ellipsoid into a Euclidean ball. By applying the same affine mapping to the data mixtures, we prove that the endmember matrix associated with the mapped data has condition number 1, the lowest possible, and that these (preconditioned) endmembers form a regular simplex. Exploiting this regular structure, we design a novel nBSS criterion with a provable identifiability guarantee and devise an algorithm to realize the criterion. Moreover, for the first time, the optimization problem for computing JE is exactly solved for a large-scale instance; our solver employs a split augmented Lagrangian shrinkage algorithm with all proximal operators solved by closed-form solutions. The competitiveness of the proposed method is illustrated by numerical simulations and real data experiments.

Popularity prediction of social posts is one of the most critical issues for social media analysis and understanding. In this paper, we discover a more dominant feature representation of text information, as well as propose a singe ensemble learning model to obtain the popularity scores, for social media prediction challenge. However, most social media prediction techniques focus on predicting the popularity score of social posts based on a single model, such as deep learning-based or ensemble learning-based approaches. However, it is well-known that the model stacking strategy is a more effective way to boost the performance on various regression tasks. In this paper, we also show that the model stacking can be modeled as a simple recurrent neural network problem with comparable performance on predicting popularity scores. Firstly, a single strong baseline is proposed based on the deep neural network with a prediction branch. Then, the partial feature maps of the last layer of our strong baseline are used to establish a new branch with an isolated predictor. It is easy to obtain multi-prediction by repeating the above two steps. These preliminary predicted scores are then formed as the input of the recurrent unit to learn the final predicted scores, called Recurrent Stacking Model (RSM). Our experiments show that the proposed ensemble learning approach outperforms other state-of-the-art methods. Furthermore, the proposed RSM also shows the superiority over our ensemble learning approach, having verified that the model stacking problem can be transformed into the training problem of a recurrent neural network.

Sentinel-2 satellite, launched by the European Space Agency, plays a critical role in various Earth observation missions. However, the spatial resolutions of Sentinel-2 images are different across its spectral bands, including four bands with a resolution of 10 m, six bands with a resolution of 20 m, and three bands with a resolution of 60 m. To facilitate the effectiveness of analyzing these images, super-resolving of the low-/medium-resolution bands to a higher resolution is desired. As in any image restoration inverse problems, we exploit image self-similarity, a commonly observed property in natural images, which underlies the state-of-the-art techniques, e.g., in image denoising. However, the design of self-similarity priors in nondiagonal inverse problems is challenging; often, a denoiser based on self-similarity is plugged into the iterations of an algorithm, without a guarantee of convergence in general. In this article, for the first time, we introduce a convex and scene-adapted regularizer built explicitly on a self-similarity graph directly learned from the Sentinel-2 images. We then develop a fast algorithm, termed Sentinel-2 super-resolution via scene-adapted self-similarity (SSSS). We experimentally show the superiority of SSSS over four commonly observed scenes, indicating the potential usage of our convex self-similarity regularization in other imaging inverse problems.

In satellite imaging remote sensing, injecting spatial details extracted from a panchromatic image into a multispectral image is referred to as pansharpening, which is ill-posed and requires regularization. Self-similarity, a critical prior knowledge yielding great success in regularizing various imaging inverse problems, has been widely observed in natural images; its formalization is not, however, straightforward. Very recently, we mathematically described the self-similarity pattern as a weighted graph, which can then be transformed into an explicit convex regularizer, that is adopted in our pansharpening criterion design. Most importantly, such convexity allows the adoption of convex optimization theory in solving self-similarity regularized inverse problems with convergence guarantee. One step of our pansharpening algorithm is exactly the proximal operator induced by our new self-similarity regularizer, which is solved by another customized algorithm that is interesting in its own right as could be used as a denoiser. Experiments show promising performance of the proposed method.

Change detection (CD), enabled by multitemporal multispectral satellite imagery, has many important Earth observation missions such as land cover/use monitoring, for which we observe that change regions are relatively smaller than those caused by disaster (e.g., forest fire) with patterns typically composed of a number of smooth regions. These observations are considered in our new CD criterion, which can effectively mitigate the artifacts and speckle noise suffered by existing statistic-based and difference image (DI) analysis based methods. The proposed CD criterion amounts to a large-scale non-convex optimization, which is first reformulated using the convex relaxation trick with associated change map interpreted in the probability sense, followed by adopting an efficient convex solver known as alternating direction method of multipliers (ADMM). The resulted probabilistic change map would be more practical, and can be thresholded at 0.5 to yield the conventional binary-valued one. We also reveal a link between the proposed criterion and the DI-based criterion, and demonstrate the outstanding performance of our fully unsupervised CD algorithm qualitatively and quantitatively.

Linear hyperspectral unmixing (HU) aims at factoring the observation matrix into an endmember matrix and an abundance matrix. Linear HU via variational minimum volume (MV) regularization has recently received considerable attention in the remote sensing and machine learning areas, mainly owing to its robustness against the absence of pure pixels. We put some popular linear HU formulations under a unifying framework, which involves a data-fitting term and an MV-based regularization term, and collectively solve it via a nonconvex optimization. As the former and the latter terms tend, respectively, to expand (reducing the data-fitting errors) and to shrink the simplex enclosing the measured spectra, it is critical to strike a balance between those two terms. To the best of our knowledge, the existing methods find such balance by tuning a regularization parameter manually, which has little value in unsupervised scenarios. In this paper, we aim at selecting the regularization parameter automatically by exploiting the fact that a too large parameter overshrinks the volume of the simplex defined by the endmembers, making many data points be left outside of the simplex and hence inducing a large data-fitting error, while a sufficiently small parameter yields a large simplex making data-fitting error very small. Roughly speaking, the transition point happens when the simplex still encloses the data cloud but there are data points on all its facets. These observations are systematically formulated to find the transition point that, in turn, yields a good parameter. The competitiveness of the proposed selection criterion is illustrated with simulated and real data.

In hyperspectral unmixing and in many other areas (e.g., chemometrics, topic modeling, archetypal analysis) simplex-structured matrix factorization (SSMF) plays an essential role as suggested by years of research efforts devoted to this theme. Specifically, SSMF factorizes a data matrix into two matrix factors with one factor (i.e., the abundances) constrained to have its columns lying in the unit simplex. SSMF criteria include the well-known Craig's seminal minimum-volume enclosing simplex (MVES), originally proposed for blind hyperspectral unmixing, and the recently introduced maximum-volume inscribed ellipsoid (MVIE). The identifiability analysis of those criteria is essential to understand their fundamental behavior and also to devise effective SSMF algorithms tailored to the specificities of the different application scenarios. Our analysis is motivated by a simple fact taking place in most remotely sensed hyperspectral mixtures: in most pixels, only a subset of the materials is present. This is to say that the abundances exhibit a form of sparsity and thus lie in the boundary of the data simplex. We then derive some elegant sufficient condition, showing that as long as data points are locally well spread, perfect SSMF identifiability of both criteria can be guaranteed.

Consider a structured matrix factorization model where one factor is restricted to have its columns lying in the unit simplex. This simplex-structured matrix factorization (SSMF) model and the associated factorization techniques have spurred much interest in research topics over different areas, such as hyperspectral unmixing in remote sensing and topic discovery in machine learning, to name a few. In this paper we develop a new theoretical SSMF framework whose idea is to study a maximum volume ellipsoid inscribed in the convex hull of the data points. This maximum volume inscribed ellipsoid (MVIE) idea has not been attempted in prior literature, and we show a sufficient condition under which the MVIE framework guarantees exact recovery of the factors. The sufficient recovery condition we show for MVIE is much more relaxed than that of separable nonnegative matrix factorization (or pure-pixel search); coincidentally, it is also identical to that of minimum volume enclosing simplex, which is known to be a powerful SSMF framework for nonseparable problem instances. We also show that MVIE can be practically implemented by performing facet enumeration and then by solving a convex optimization problem. The potential of the MVIE framework is illustrated by numerical results.

Fusing a low-spatial-resolution hyperspectral data with a high-spatial-resolution (HSR) multispectral data has been recognized as an economical approach for obtaining HSR hyperspectral data, which is important to accurate identification and classification of the underlying materials. A natural and promising fusion criterion, called coupled nonnegative matrix factorization (CNMF), has been reported that can yield high-quality fused data. However, the CNMF criterion amounts to an ill-posed inverse problem, and hence, advisable regularization can be considered for further upgrading its fusion performance. Besides the commonly used sparsity-promoting regularization, we also incorporate the well-known sum-of-squared-distances regularizer, which serves as a convex surrogate of the volume of the simplex of materials’ spectral signature vectors (i.e., endmembers), into the CNMF criterion, thereby leading to a convex formulation of the fusion problem. Then, thanks to the biconvexity of the problem nature, we decouple it into two convex subproblems, which are then, respectively, solved by two carefully designed alternating direction method of multipliers (ADMM) algorithms. Closed-form expressions for all the ADMM iterates are derived via convex optimization theories (e.g., Karush–Kuhn–Tucker conditions), and furthermore, some matrix structures are employed to obtain alternative expressions with much lower computational complexities, thus suitable for practical applications. Some experimental results are provided to demonstrate the superior fusion performance of the proposed algorithm over state-of-the-art methods.

While non-negative blind source separation (nBSS) has found many successful applications in science and engineering, model order selection, determining the number of sources, remains a critical yet unresolved problem. Various model order selection methods have been proposed and applied to real-world data sets but with limited success, with both order over- and under-estimation reported. By studying existing schemes, we have found that the unsatisfactory results are mainly due to invalid assumptions, model oversimplification, subjective thresholding, and/or to assumptions made solely for mathematical convenience. Building on our earlier work that reformulated model order selection for nBSS with more realistic assumptions and models, we report a newly and formally revised model order selection criterion rooted in the minimum description length (MDL) principle. Adopting widely invoked assumptions for achieving a unique nBSS solution, we consider the mixing matrix as consisting of deterministic unknowns, with the source signals following a multivariate Dirichlet distribution. We derive a computationally efficient, stochastic algorithm to obtain approximate maximum-likelihood estimates of model parameters and apply Monte Carlo integration to determine the description length. Our modeling and estimation strategy exploits the characteristic geometry of the data simplex in nBSS. We validate our nBSS-MDL criterion through extensive simulation studies and on four real-world data sets, demonstrating its strong performance and general applicability to nBSS. The proposed nBSS-MDL criterion consistently detects the true number of sources, in all of our case studies.

Heterogeneous network (HetNet), employing massive multiple-input multiple-output (MEMO), has been recognized as a promising technique to enhance network capacity, and to improve energy efficiency for fifth generation (5G) of wireless communications. However, most existing schemes for coordinated beamforming (CoBF) for a massive MIMO HetNet unrealistically assume the availability of perfect channel state information (CSQ on one hand, and cascade of each antenna with a distinct radio frequency (RF) chain in massive MEMO is neither power nor cost efficient on the other hand. In this paper, we consider a massive MEMO enabled HetNet framework, consisting of one macrocell base station (MBS) equipped with an analog beamformer, followed by a digital beamformer, and one femtocell base station (FBS) equipped with a digital beamformer. In the presence of Gaussian CSI errors, we propose a robust hybrid CoBF (HyCoBF) design, including an analog beamforming design for MBS and a digital CoBF design for both MBS and FBS. To this end, an outage probability constrained robust HyCoBF problem is formulated by minimizing the total transmit power. The analog beamforming mechanism at MBS is a newly devised low-complexity beam selection scheme by selecting analog beams from a discrete Fourier transform (DFT) matrix codebook. Then a conservative approximate CoBF solution is obtained via semidefinite relaxation (SDR) and an extended Bernsteintype inequality. Finally, numerical simulations are provided to demonstrate the efficacy of the proposed HyCoBF algorithm.

Hyperspectral unmixing (HU) is an essential signal processing procedure for blindly extracting the hidden spectral signatures of materials (or endmembers) from observed hyperspectral imaging data. Craig's criterion, stating that the vertices of the minimum volume enclosing simplex (MVES) of the data cloud yield high-fidelity endmember estimates, has been widely used for designing endmember extraction algorithms (EEAs) especially in the scenario of no pure pixels. However, most Craig-criterion-based EEAs generally suffer from high computational complexity due to heavy simplex volume computations, and performance sensitivity to random initialization, etc. In this work, based on the idea that Craig's simplex with N vertices can be defined by N associated hyperplanes, we develop a fast and reproducible EEA by identifying these hyperplanes from N(N - 1) data pixels extracted via simple and effective linear algebraic formulations, together with endmember identifiability analysis. Some Monte Carlo simulations are provided to demonstrate the superior efficacy of the proposed EEA over state-of-the-art Craig-criterion-based EEAs in both computational efficiency and estimation accuracy.

In blind hyperspectral unmixing (HU), the pure-pixel assumption is well known to be powerful in enabling simple and effective blind HU solutions. However, the pure-pixel assumption is not always satisfied in an exact sense, especially for scenarios where pixels are heavily mixed. In the no-pure-pixel case, a good blind HU approach to consider is the minimum volume enclosing simplex (MVES). Empirical experience has suggested that MVES algorithms can perform well without pure pixels, although it was not totally clear why this is true from a theoretical viewpoint. This paper aims to address the latter issue. We develop an analysis framework wherein the perfect endmember identifiability of MVES is studied under the noiseless case. We prove that MVES is indeed robust against lack of pure pixels, as long as the pixels do not get too heavily mixed and too asymmetrically spread. The theoretical results are supported by numerical simulation results.

Hyperspectral unmixing (HU) is a process to extract the underlying endmember signatures (or simply endmembers) and the corresponding proportions (abundances) from the observed hyperspectral data cloud. The Craig's criterion (minimum volume simplex enclosing the data cloud) and the Winter's criterion (maximum volume simplex inside the data cloud) are widely used for HU. For perfect identifiability of the endmembers, we have recently shown in [1] that the presence of pure pixels (pixels fully contributed by a single endmember) for all endmembers is both necessary and sufficient condition for Winter's criterion, and is a sufficient condition for Craig's criterion. A necessary condition for endmember identifiability (EI) when using Craig's criterion remains unsolved even for three-endmember case. In this work, considering a three-endmember scenario, we endeavor a statistical analysis to identify a necessary and statistically sufficient condition on the purity level (a measure of mixing levels of the endmembers) of the data, so that Craig's criterion can guarantee perfect identification of endmembers. Precisely, we prove that a purity level strictly greater than 1/√(2) is necessary for EI, while the same is sufficient for EI with probability-1. Since the presence of pure pixels is a very strong requirement which is seldom true in practice, the results of this analysis foster the practical applicability of Craig's criterion over Winter's criterion, to real-world problems.

a programmable dual hysteretic window comparator is presented in this paper. The comparator uses a cascoded flipped voltage follower (CASFVF), a high speed VI converter, and a current comparator to enhance the response time and accuracy. Moreover, the positive and negative hysteretic thresholds can be programmable, respectively. Simulation results in 0.25-μm CMOS technology demonstrate the validity of the designed approach.