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The pervasive presence of mixed pixels in hyperspectral remote sensing imagery poses a substantial constraint on the quantitative progress of remote sensing technology. Hyperspectral unmixing (HU) techniques serve as effective means to address this issue. In recent years, deep learning methods, particularly autoencoders (AEs), have been progressively employed in blind HU due to their compatibility with linear mixture models. However, most of the current advanced AE unmixing networks are based on a single-stage framework that conducts the unmixing task solely from a spectral perspective. This makes the rich spatial information ignored and makes it difficult for the network to obtain discriminative compression features while being susceptible to spectral variability and noise outliers. To address these issues, we propose a new deep shared fully connected autoencoder (DSFC-AE) unmixing network. The proposed DSFC-AE network comprises dual branches that utilize distinct data inputs for feature extraction: the original spectral data and coarse-scale spectral data obtained through superpixel segmentation. Furthermore, shared weight strategies are applied to the corresponding dimension reduction layers of the encoder, facilitating effective feature fusion. In addition, we integrate two constraint terms into the loss function, harnessing the sparsity of abundances and the geometric features of endmembers. We evaluate the DSFC-AE method against three traditional methods and four state-of-the-art deep learning algorithms using multiple real datasets. The results unequivocally demonstrate that the proposed network achieves significant improvements in both accuracy and stability.

Hyperspectral unmixing (HU), an essential procedure for various environmental applications, has garnered significant attention within remote sensing communities. Among different groups of HU methods, nonnegative matrix factorization (NMF)-based ones have gained widespread popularity due to their high capability of simultaneously extracting endmembers and their corresponding abundances. However, converting a 3-D hyperspectral data cube into a 2-D matrix format leads to the loss of spatial and potential correlation information. Consequently, in recent years, nonnegative tensor factorization (NTF) methods, which preserve the 3-D nature of hyperspectral data cube, have been extensively embraced by numerous researchers. Nevertheless, incorporating prior information into NTF-based problems faces limitations owing to the inconsistency of such information, particularly concerning $\ell _{1}$ norm sparsity and the abundance sum-to-one constraint (ASC). To address this limitation, our study introduces a novel general regularization term. This term leverages sparsity and ASC simultaneously, integrating it into a matrix-tensor factorization framework. Our proposed method, named a matrix-tensor-based HU method with general $\ell _{q}$ norm regularization (MTUHL$_{q}$), is established on the block term decomposition (BTD) paradigm, which ensures physical interpretability and simple implementation. To investigate the performance of the proposed MTUHL$_{q}$, a series of experiments on both synthetic and real hyperspectral datasets were conducted. The results of the implemented experiments indicated that the proposed method outperformed other state-of-the-art HU methods.

The purpose of hyperspectral unmixing (HU) is to extract the spectral signatures and their proportion fractions from the hyperspectral remote sensing image (HSIs), which is a crucial issue in HSIs processing. Recently, nonnegative tensor factorization (NTF) has been successfully applied in the field of HU, because a third-order tensor can effectively maintain the spatial–spectral structure of HSIs, and NTF can produce multiple-view factor matrices that can impose more natural and diverse constraints. However, current NTF unmixing models utilizing priors are still insufficient, and NTF does not fully utilize the multiview factor matrices. Moreover, most methods only consider single-factor constraints, neglecting the effectiveness of collaborative constraints among multiple-factor priors information. To address the aforementioned shortcomings, a reweighted unidirectional total variation (UTV) low-rank NTF with multiple-factor collaborative regularization is proposed in this article. Specifically, first, to further exploit the abundance prior information, by utilizing the spatial similarity and the group sparse structure between the pixels of the two abundance low-rank submatrices, two reweighted UTV regularizers are constructed, which enhance the smooth and sparse properties of the abundances. Second, to smooth the endmember spectra and reduce the irregular burrs phenomenon caused by spectral noise interference, we introduce endmember band difference smooth constraints to ensure the piecewise smoothness of the endmember spectrum. Then, two reweighted UTV regularizers and an endmember spectral smooth regularizer are jointly introduced into the low-rank NTF framework to collaboratively regularize the nonconvex tensor representation model. Finally, we adopt the alternating direction multiplier method to optimize the objective model, and a large number of experiments on both synthetic and real hyperspectral datasets validate the effectiveness and efficiency of the proposed approach.

Deep learning has gained popularity in hyperspectral unmixing (HU) applications recently due to its powerful learning and data-fitting capabilities. As an unmixing baseline network, the autoencoder (AE) framework performs well in HU by automatically learning low-dimensional embeddings and reconstructing data. Nevertheless, there are spectral variability and nonlinear mixing problems in the highly mixed region of hyperspectral images, which can cause interference to structures using only AE. Therefore, inspired by the effectiveness of mask modeling, we propose a multiscale convolutional mask network (MsCM-Net) for HU with two new strategies. First, we propose a mixed region mask strategy suitable for the HU task, and a multiscale convolutional AE is adopted as the unmixing baseline network to apply the mask strategy, making the method more robust in solving ill-posed unmixing problems. In addition, a new initialization strategy is used in which vertex component analysis (VCA) is combined with density-based spatial clustering of applications with noise (DBSCAN) to mitigate the impact of outliers and noise on initialization. The proposed MsCM-Net performs more accurately than state-of-the-art methods by comparison experiments on one synthetic and three real hyperspectral data sets. The effectiveness of the mixed region mask strategy and DBSCAN-VCA initialization is also demonstrated by ablation experiments.

Hyperspectral unmixing is to decompose the mixed pixel into the spectral signatures (endmembers) with their corresponding abundances. However, the ignorance of endmember variability in hyperspectral unmixing results in low performance. To solve this problem, a multi-scale convolution attention network containing endmember unmixing network (EU-Net) and abundance unmixing network, which was called as-the hyperspectral unmixing with multi-scale convolution attention network (HUMSCAN) was proposed in this article. The EU-Net is composed of the variational autoencoder and the multi-scale effective convolution block attention module (MSECBAM), which is combined with the S-VCA pretraining to adaptively extract endmembers at the pixel and subpixel levels. The AU-Net is based on the MSECBAM frame jointed the spectral and spatial attention features. The proposed HUMSCAN method can simultaneously and unsupervisedly extract endmembers and their corresponding abundances, which can improve the accuracy and efficiency of spectral unmixing. The performance of the proposed method is evaluated both on synthetic and real datasets. Experimental results show its superiority in comparison with other state-of-the-art methods.

Hyperspectral remote sensing images have received extensive attention because of their high spectral resolution. However, the limitation of spatial resolution of imaging spectrometers results in a large number of mixed pixels, which restricts the accuracy of data processing. Consequently, hyperspectral unmixing (HU) becomes an important step and tool in remote sensing image processing. In recent years, many approaches based on sparse nonnegative matrix factorization (NMF) have been widely applied in the field of HU due to their explicit statistical properties. In particular, methods based on $\ell _{1/2}$ norm regularized NMF and their extended models have attracted considerable attention. However, the $\ell _{1/2}$ sparse regularizer leads to a nonconvex and nonsmooth problem, which is a significant challenge to solve quickly and efficiently in practice. In this article, to solve the abovementioned problems, we propose a new fast $\ell _{1/2}$ sparse NMF algorithm, called NewSpr-NMF, which combines two famous fast gradient strategies, i.e., Barzilai–Borwein gradient and Nesterov's optimal gradient, to alternately optimize two subproblems in NMF framework under the block coordinate descent scheme. Specifically, for the abundance subproblem of sparse NMF, in order to accelerate the solving process, we use Barzilai–Borwein gradient technology to develop a half-thresholding approximate iterative subalgorithm, while for another endmember subproblem, we adopt the Nestrov's optimal gradient method with second-order convergence to solve. Finally, we integrate the two aforementioned algorithms together to achieve efficient unmixing by alternately optimizing the two subproblems of the sparse NMF. The computational complexity and convergence of the proposed algorithm are carefully analyzed and briefly proved theoretically, respectively. A series of experimental results on both synthetic and real datasets, and compared with other advanced approaches, verify the effectiveness and efficiency of the proposed algorithm.

In recent years, deep learning has received tremendous attention in the field of hyperspectral unmixing (HU) due to its powerful learning capabilities. Particularly, the unsupervised unmixing method based on an autoencoder (AE) has become a research hotspot. Most of the current AE unmixing networks mainly focus on information about pixels and their neighborhoods in images. However, they make insufficient use of information about spatial heterogeneity and spectral differences of endmembers in hyperspectral image (HSI) data. To this end, an AE HU network with the name of SSF-Net is proposed for fusing the spatial–spectral features. The network first extracts pseudoendmember information from the HSI using a regional vertex component analysis algorithm. Then, a dual-branch feature fusion module incorporating a spatial–spectral attention mechanism is constructed to make full use of the information in the HSI data, thereby improving the network's unmixing performance. It is worth stating that SSF-Net can fuse spatial–spectral information and utilize different attention maps to obtain more significant spectral difference information and more discriminative spatial difference information about the scene. The experimental results on synthetic and real datasets demonstrate that the proposed SSF-Net outperforms state-of-the-art unmixing algorithms.

Hyperspectral imaging captures detailed spectral data for remote sensing. However, due to the limited spatial resolution of hyperspectral sensors, each pixel of a hyperspectral image (HSI) may contain information from multiple materials. Although the hyperspectral unmixing (HU) process involves estimating endmembers, identifying pure spectral components, and estimating pixel abundances, existing algorithms mostly focus on just one or two tasks. Blind source separation (BSS) based on nonnegative matrix factorization (NMF) algorithms identify endmembers and their abundances at each pixel of HSI simultaneously. Although they perform well, the factorization results are unstable, require high computational costs, and are difficult to interpret from the original HSI. CUR matrix decomposition selects specific columns and rows from a dataset to represent it as a product of three small submatrices, resulting in interpretable low-rank factorization. In this paper, we propose a new blind HU framework based on CUR factorization called CUR-HU that performs the entire HU process by exploiting the low-rank structure of given HSIs. CUR-HU incorporates several techniques to perform the HU process with a performance comparable to state-of-the-art methods but with higher computational efficiency. We adopt a deterministic sampling method to select the most informative pixels and spectrum components in HSIs. We use an incremental QR decomposition method to reduce computation complexity and estimate the number of endmembers. Various experiments on synthetic and real HSIs are conducted to evaluate the performance of CUR-HU. CUR-HU performs comparably to state-of-the-art methods for estimating the number of endmembers and abundance maps, but it outperforms other methods for estimating the endmembers and the computational efficiency. It has a 9.4 to 249.5 times speedup over different methods for different real HSIs. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing is to decompose the mixed pixel into the spectral signatures (endmembers) with their corresponding abundances. However, the ignorance of endmember variability in hyperspectral unmixing results in low performance. To solve this problem, a multi-scale convolution attention network containing endmember unmixing network (EU-Net) and abundance unmixing network, which was called as-the hyperspectral unmixing with multi-scale convolution attention network (HUMSCAN) was proposed in this article. The EU-Net is composed of the variational autoencoder and the multi-scale effective convolution block attention module (MSECBAM), which is combined with the S-VCA pretraining to adaptively extract endmembers at the pixel and subpixel levels. The AU-Net is based on the MSECBAM frame jointed the spectral and spatial attention features. The proposed HUMSCAN method can simultaneously and unsupervisedly extract endmembers and their corresponding abundances, which can improve the accuracy and efficiency of spectral unmixing. The performance of the proposed method is evaluated both on synthetic and real datasets. Experimental results show its superiority in comparison with other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) based on the linear mixing model (LMM) has received much attention in the remote sensing community over the past decades. However, many HU algorithms are based on the fixed endmember and do not fully exploit the inherent spatial characteristics of the hyperspectral image (HSI). In this letter, a new HU algorithm named graph Laplacian regularization based on $l_{1}$ -norm-Gaussian mixture model (GLR $_{l_{1}}$ -GMM) is proposed to solve these problems. We use GMM to represent the endmember variability. Then, considering the local smoothness in the abundance map, a GLR $_{l_{1}}$ is embedded in the prior abundance. Under the Bayesian framework, the objective density function leads to a maximum posterior (MAP) problem, which can be solved by a generalized expectation–maximization (GEM) algorithm. Experiments on two real datasets demonstrate the effectiveness of the proposed algorithm compared with other state-of-the-art methods. The source code is available at https://github.com/lwdinwhu/GMM-GLRl1. [ABSTRACT FROM AUTHOR]

Autoencoders (AEs) are widely utilized in hyperspectral unmixing (HU) as an unsupervised learning model. In particular, convolutional AE networks are popular for processing multidimensional hyperspectral features. Nonetheless, the traditional convolutional AE network’s receptive field is constrained in the unmixing task, and establishing the connection between the local spatial neighborhood and the local spectrum fails to improve unmixing performance significantly. To address these limitations, a bilateral global attention network based on both spatial and spectral information is proposed. It enables the network to obtain respective feature dependencies in the two dimensions and achieve optimal fusion of both features. The network comprises two information extraction branches. The spatial information extraction branch uses the Swin Transformer block to acquire the global spatial attention of the overall image, while the spectral information extraction branch designates a simplified spectral channel attention mechanism to gain spectral attention weight maps. The network’s efficacy is demonstrated through a comparative study using a synthetic dataset and two real datasets. The code of this work is available at https://github.com/UPCGIT/SSABN. [ABSTRACT FROM AUTHOR]

Endmember extraction (EE) is a key task for hyperspectral image (HSI) unmixing. The majority of EE algorithms extract only one pure spectrum for each class of material, which may lead to a large unmixing error in cases of spectral variability. Endmember bundle extraction (EBE), which identifies a set of endmembers representing the spectral variability within each class, has been developed to solve the spectral variability problem. To date, only a small number of EBE methods have been developed; moreover, these approaches mainly employ traditional convex-geometry-based EE methods to extract endmember bundles from subset data, which may result in the loss of some endmembers and an incomplete endmember bundle set. This letter proposes an improved multiobjective particle swarm optimization method for the identification of multiple endmember bundles, named IMPSO-EBE. The proposed approach follows the framework of the spatial-spectral EBE (SSEBE) method, which extracts endmember candidates first and then applies post-processing to remove redundant endmembers. However, unlike the SSEBE method, which uses the traditional pixel purity index (PPI) method to obtain candidate endmembers from single feature space, IMPSO-EBE proposes to cooperate across multiple dataspaces to obtain candidate endmembers based on multiobjective particle swarm optimization, making it able to extract candidate endmembers that cannot be identified in single feature space. We compare the performance of the proposed method with that of the single dataspace-based EBE methods using two real hyperspectral datasets. Results show that the endmember bundles identified by the proposed method are more complete than those of the comparison method. [ABSTRACT FROM AUTHOR]

With the support of spectral libraries, sparse unmixing techniques have gradually developed. However, some existing sparse unmixing algorithms suffer from problems, such as insufficient utilization of spatial information and sensitivity to noise. To solve these problems, this article proposes a novel hyperspectral unmixing algorithm, called superpixel-based weighted sparse regression and spectral similarity constrained unmixing. In the proposed method, a precalculated weight is introduced to help enhance sparsity of abundances, which is obtained from coarse abundance estimation. It also maintains spatial consistency in a local region of a hyperspectral image to mitigate the negative influence of noise. Additionally, the method selects optimal neighborhood pixels in the local region by combining spatial and spectral information and constructs a similarity matrix to explore spectral similarity in the subspace. Meanwhile, superpixel segmentation is considered as an auxiliary method to obtain local regions in the unmixing process. Experiments performed on synthetic and real data demonstrate that the proposed method achieves more accurate abundance estimation than other comparison algorithms.

Hyperspectral imaging captures detailed spectral data for remote sensing. However, due to the limited spatial resolution of hyperspectral sensors, each pixel of a hyperspectral image (HSI) may contain information from multiple materials. Although the hyperspectral unmixing (HU) process involves estimating endmembers, identifying pure spectral components, and estimating pixel abundances, existing algorithms mostly focus on just one or two tasks. Blind source separation (BSS) based on nonnegative matrix factorization (NMF) algorithms identify endmembers and their abundances at each pixel of HSI simultaneously. Although they perform well, the factorization results are unstable, require high computational costs, and are difficult to interpret from the original HSI. CUR matrix decomposition selects specific columns and rows from a dataset to represent it as a product of three small submatrices, resulting in interpretable low-rank factorization. In this paper, we propose a new blind HU framework based on CUR factorization called CUR-HU that performs the entire HU process by exploiting the low-rank structure of given HSIs. CUR-HU incorporates several techniques to perform the HU process with a performance comparable to state-of-the-art methods but with higher computational efficiency. We adopt a deterministic sampling method to select the most informative pixels and spectrum components in HSIs. We use an incremental QR decomposition method to reduce computation complexity and estimate the number of endmembers. Various experiments on synthetic and real HSIs are conducted to evaluate the performance of CUR-HU. CUR-HU performs comparably to state-of-the-art methods for estimating the number of endmembers and abundance maps, but it outperforms other methods for estimating the endmembers and the computational efficiency. It has a 9.4 to 249.5 times speedup over different methods for different real HSIs.

Hyperspectral unmixing aims to separate pure materials and their corresponding proportions that constitute the mixed pixels of hyperspectral imagery (HSI). Recently, the matrix-vector nonnegative tensor factorization (MV-NTF) has attracted wide attention in this field due to its natural third-tensor representation of HSI. However, the NTF-based unmixing approaches are limited to the nonunique solution and long computational time. To solve these problems, we consider the low-rank and sparse priors of each abundance map simultaneously and propose a new unmixing model adopting a weighted nuclear norm and an $L_{1/2}$ norm under the MV-NTF framework. Instead of using low-rank matrix decomposition of MV-NTF, this model imposes the low-rank property on the whole abundance map, which avoids determining the rank of the abundance map in advance. Observing that each abundance map is different, we build an adaptive update mechanism to treat each low-rank and sparse constraint differently in the model. Furthermore, a new multiplicative iterative algorithm is designed to solve the proposed model. Specially, the algorithm designed for this tensor model is simplified by using the equivalence relation with nonnegative matrix factorization. Experiments demonstrate that the proposed method is effective in improving both the unmixing effect and the solving speed.

Neural networks have been widely applied in hyperspectral unmixing in the past few years. However, most networks only focus on extracting the spectral information or local spectral–spatial correlation of a single pixel. In order to further explore the spectral–spatial information of hyperspectral images (HSIs) and improve the effective use of spatial information in unmixing tasks, an end-to-end semisupervised unmixing network is proposed in this article. At the encoder, the dual branch network performs convolution operations along the spatial dimension and the spectral dimension, respectively, to realize the separated extraction of global spatial and spectral information; the spectral–spatial attention residual module then fuses the separated spectral–spatial features into the joint spectral–spatial information. The encoder is to realize mapping from high-dimensional spectral data to latent abundance representations. The decoder is a simple linear fully connected layer whose weight is fixed to a known spectral library to complete the reconstruction of the HSI. Experiments on two synthetic datasets and two real datasets demonstrate the superior performance of the proposed method, and prove the effectiveness of considering global spatial information in the unmixing task.

Due to the powerful and automatic representation capabilities, deep learning (DL) techniques have made significant breakthroughs and progress in hyperspectral unmixing (HU). Among the DL approaches, autoencoders (AEs) have become a widely used and promising network architecture. However, these AE-based methods heavily rely on manual design and may not be a good fit for specific datasets. To unmix hyperspectral images more intelligently, we propose an automatic neural architecture search model for HU, AutoNAS for short, to determine the optimal network architecture by considering channel configurations and convolution kernels simultaneously. In AutoNAS, the self-supervised training mechanism based on hyperspectral images is first designed for generating the training samples of the supernet. Then, the affine parameter sharing strategy is adopted by applying different affine transformations on the supernet weights in the training phase, which enables finding the optimal channel configuration. Furthermore, on the basis of the obtained channel configuration, the evolutionary algorithm with additional computational constraints is introduced into networks to achieve flexible convolution kernel search by evaluating unmixing results of different architectures in the supernet. Extensive experiments conducted on four hyperspectral datasets demonstrate the effectiveness and superiority of the proposed AutoNAS in comparison with several state-of-the-art unmixing algorithms. [ABSTRACT FROM AUTHOR]

In HSI, the unmixing of images plays an imperative role since the initial years. The collection of spectral signatures from the existing environments is perpetually its fusion of several constituents originated in the spatial range. HSI obtains a three-dimensional dataset called hypercube, having one spectral and two spatial dimensions. The exploration of HSI is based on the spectral decay of the pixels through the spectral unmixing method, having applications in detection of the target, unsupervised segmentation of the image, etc. The perilous part is to define the endmembers used as the references for the process of unmixing. Hence, inclusive details of the unmixing method are required as its application is extensively growing. The unmixing methods are summarized in three categories: extraction of endmember, selection of endmember combinations, and abundance estimation. The paper consequently provides an outline of HSI unmixing and its applications. The primary objective is to provide a historical outline of the popular methods of unmixing and to discuss certain popular techniques in detail. In HSI unmixing, LMM is the dominant archetypal besides it is a foundation of a huge diversity of unmixing methods in HSI, hence a prominent part of the review embraces it. Furthermore, in the HSI unmixing, nonlinearity is a critical factor in real-world situations. While numerous models for nonlinear unmixing are projected, in recent times there occurred an explosion of nonlinear models for unmixing. Henceforth, we deliver an outline of some recent expansions in the nonlinear unmixing literature. The objective of the paper is threefold: an overview for new researchers and for those already functioning and searching for literature in this arena. The quantitative measure of certain existing methods helps to analyze current progress and to anticipate imminent growth. Lastly, the review is structured according to the elementary computational method of unmixing: geometrical, statistical, and heuristic approaches with a small segment of statistical versus geometrical methods. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) has been a hot research topic in the field of hyperspectral remote sensing. In recent years, the employment of the probabilistic topic model to acquire the latent topics of hyperspectral images has been an effective method for spectral unmixing. However, such methods fail to fully exploit the potential of topic models in uncovering image semantics, and they need extra sparsity constraints, which greatly increases the complexity of the model. To solve these problems, a sparse topic relaxion and group clustering model for HU (STRGC) is proposed. In STRGC, the sparse prior constraints implied by the sparse topic model are introduced, which means that the sparse characteristics of the model are used to capture the semantic representation of the spectrum. Through the relaxation of the model, the possible spectral representations of ground features can be obtained, and this further alleviates the influence caused by endmember variability on the accuracy of the unmixing process. Then, fuzzy clustering is used to locate the position of the endmember quickly and accurately. Furthermore, unmixing models with different characteristics are united to alleviate the ill-posed nature of the model, thereby improving the fractional abundance. Experimental results obtained with one simulated dataset and three well-known real hyperspectral datasets confirm the effectiveness and advantages of the proposed method.

Detecting underwater targets from hyperspectral imagery makes a profound impact on marine exploration. Available methods mainly tackle this problem by modifying the land-based detection algorithms with classical bathymetric models, which usually fail to remove the interference of background and ignore the effect of depth information, leading to a poor detection performance. To achieve a more precise result, in this work we propose a novel network based on hyperspectral unmixing (HU) methodology and bathymetric models to detect the desired underwater targets. The proposed network, called underwater target detection network (UTD-Net), first develops a novel joint anomaly detector with classical HU methods to separate out target-water mixed pixels, which is devoted to eliminate the adverse influence of background. Then, we explore a bathymetric model-based autoencoder to unmix the target-water mixed pixels for acquiring the target-associated abundance values and maps. One dimension convolutional neural network is exploited to construct the encoder part of above autoencoder for the sake of addressing spectral variability problem. Moreover, considering the physical meaningless endmembers issue, a particular spectral constraint is imposed on the objective function as a training guidance. In this way, the autoencoder would be capable of generating specific endmembers and their corresponding abundance maps. Finally, according to the physical essence of abundance maps, we figure out the detection result by fusing the outcomes of autoencoder with weight coefficients determined by abundance values. Qualitative and quantitative illustrations demonstrate the effectiveness and efficiency of UTD-Net in comparison with the state-of-the-art underwater target detection methods.

Hyperspectral unmixing (HU) has become an important technique in exploiting hyperspectral data since it decomposes a mixed pixel into a collection of endmembers weighted by fractional abundances. The endmembers of a hyperspectral image (HSI) are more likely to be generated by independent sources and be mixed in a macroscopic degree before arriving at the sensor element of the imaging spectrometer as mixed spectra. Over the past few decades, many attempts have focused on imposing auxiliary regularizes on the conventional nonnegative matrix factorization (NMF) framework in order to effectively unmix these mixed spectra. As a promising step toward finding an optimum regularizer to extract endmembers, this article presents a novel blind HU algorithm, referred to as kurtosis-based smooth nonnegative matrix factorization (KbSNMF) which incorporates a novel regularizer based on the statistical independence of the probability density functions of endmember spectra. Imposing this regularizer on the conventional NMF framework promotes the extraction of independent endmembers while further enhancing the parts-based representation of data. Experiments conducted on diverse synthetic HSI datasets (with numerous numbers of endmembers, spectral bands, pixels, and noise levels) and three standard real HSI datasets demonstrate the validity of the proposed KbSNMF algorithm compared to several state-of-the-art NMF-based HU baselines. The proposed algorithm exhibits superior performance especially in terms of extracting endmember spectra from hyperspectral data; therefore, it could uplift the performance of recent deep learning HU methods which utilize the endmember spectra as supervisory input data for abundance extraction.

Hyperspectral unmixing (HU) has been one of the most significant tasks in hyperspectral image (HSI) processing. In recent years, nonnegative matrix factorization (NMF) has received great attention in the HU due to its simultaneous estimation, flexible modeling, and little requirement on prior information. However, several common NMF algorithms still suffer from high computational complexity, instability, and low convergence rate. Motivated by the matrix manifold theory, this article proposes a new sparse oblique-manifold ($\mathcal {OB}$) NMF method from the perspective of matrix manifold. The critical idea of the proposed method is to regard the abundance matrix as locating on the oblique manifold, which eliminates its constraint of nonnegativity and sum-to-one and incorporates its intrinsic Riemannian geometry. Meanwhile, the $L_{1/2}$ -norm on the Euclidean space can be transformed equivalently into the $L_{1}$ -norm on oblique manifold. Then, via solving this sparse $\mathcal {OB}$ NMF by the Riemannian conjugated gradient (RCG) algorithm and the multiplicative iterative rule, the proposed method not only ensures improvement in the solution accuracy but also leads to a much faster convergence rate. Experimental results from the synthetic and real-world datasets illustrate the effectiveness and efficiency of the proposed method compared with the state-of-the-art NMF methods in HU. [ABSTRACT FROM AUTHOR]

In recent years, deep learning (DL) has attracted increasing attention in hyperspectral unmixing (HU) applications due to its powerful learning and data fitting ability. The autoencoder (AE) framework, as an unmixing baseline network, achieves good performance in HU by automatically learning low-dimensional embeddings and reconstructing data. Nevertheless, the conventional AE-based architecture, which focuses more on the pixel-level reconstruction loss, tends to lose some significant detailed information of certain materials (e.g., material-related properties) in the reconstruction process. Therefore, inspired by the perception mechanism, we propose a cycle-consistency unmixing network, called CyCU-Net, by learning two cascaded AEs in an end-to-end fashion, to enhance the unmixing performance more effectively. CyCU-Net is capable of reducing the detailed and material-related information loss in the process of reconstruction by relaxing the original pixel-level reconstruction assumption to cycle consistency dominated by the cascaded AEs. More specifically, cycle consistency can be achieved by a newly proposed self-perception loss, which consists of two spectral reconstruction terms and one abundance reconstruction term. By taking advantage of the self-perception loss in the network, the high-level semantic information can be well preserved in the unmixing process. Moreover, we investigate the performance gain of CyCU-Net with extensive ablation studies. Experimental results on one synthetic and three real hyperspectral data sets demonstrate the effectiveness and competitiveness of the proposed CyCU-Net in comparison with several state-of-the-art unmixing algorithms. [ABSTRACT FROM AUTHOR]

Over the past decades, numerous methods have been proposed to solve the linear or nonlinear mixing problems in hyperspectral unmixing (HU). The existence of spectral variabilities and nonlinearity limits, to a great extent, the unmixing ability of most traditional approaches, particularly in complex scenes. In recent years, deep learning (DL) has been garnering increasing attention in nonlinear HU owing to its powerful learning and fitting ability. However, the DL-based methods tend to generate trivial unmixing results due to the lack of considering physically meaningful endmember information. To this end, we propose a novel siamese network, called the deep half-siamese network (Deep HSNet), for HU by fully considering diverse endmember properties extracted using different endmember extraction algorithms. Moreover, the proposed Deep HSNet, beyond the previous autoencoder-like architecture, adopts another subnetwork to learn the endmember information effectively to guide the unmixing process in a reasonable and accurate way. The experimental results conducted on the synthetic and real hyperspectral data sets validate the effectiveness and superiority of the Deep HSNet over several state-of-the-art unmixing algorithms. [ABSTRACT FROM AUTHOR]

Most image fusion algorithms based on hyperspectral unmixing perform worse with the lower spatial resolution of hyperspectral image (HSI) for the reason that the estimated endmembers and abundance deviate from the truth value. Therefore, it is more meaningful to unmix the low spatial resolution hyperspectral image (LRHSI) accurately, which is also helpful to improve the image fusion performance. In order to enhance the spatial resolution of LRHSI, this article proposes an alternating direction iterative nonnegative matrix factorization (ADINMF) based on linear hyperspectral unmixing algorithm. It takes multispectral image as a constraint to improve the spatial resolution of LRHSI. First, we use blind source separation to initialize the endmember and abundance of hyperspectral and multispectral images, respectively. Then, we alternately update the endmembers and abundance in the framework of nonnegative matrix factorization by multiplication iterative algorithm. The updated endmembers and abundance are constrained to each other. We compare the experimental results of simulated dataset and three groups of real datasets. Experimental results show that the proposed method not only accurately extracts the endmembers of LRHSI, but also obtains a significant fusion performance improvement.

Hyperspectral unmixing is a crucial task for hyperspectral images (HSIs) processing, which estimates the proportions of constituent materials of a mixed pixel. Usually, the mixed pixels can be approximated using a linear mixing model. Since each material only occurs in a few pixels in real HSI, sparse nonnegative matrix factorization (NMF), and its extensions are widely used as solutions. Some recent works assume that materials are distributed in certain structures, which can be added as constraints to sparse NMF model. However, they only consider the spatial distribution within a local neighborhood and define the distribution structure manually, while ignoring the real distribution of materials that is diverse in different images. In this article, we propose a new unmixing method that learns a subspace structure from the original image and incorporate it into the sparse NMF framework to promote unmixing performance. Based on the self-representation property of data points lying in the same subspace, the learned subspace structure can indicate the global similar graph of pixels that represents the real distribution of materials. Then the similar graph is used as a robust global spatial prior which is expected to be maintained in the decomposed abundance matrix. The experiments conducted on both simulated and real-world HSI datasets demonstrate the superior performance of our proposed method.

Determining the optimal number of endmember sources, which is also called “virtual dimensionality” (VD), is a priority for hyperspectral unmixing (HU). Although the VD estimation directly affects the HU results, it is usually solved independently of the HU process. In this article, a saliency-based autonomous endmember detection (SAED) algorithm is proposed to jointly estimate the VD in the process of endmember extraction (EE). In SAED, we first demonstrate that the abundance anomaly (AA) value is an important feature of undetected endmembers since pure pixels have larger AA values than “distractors” (i.e., mixed pixels and pure pixels of detected endmembers). Then, motivated by the fact that endmembers usually gather in certain local regions (superpixels) in the scene, due to spatial correlation, a superpixel prior is introduced in SAED to distinguish endmembers from noise. Specifically, the undetected endmembers are defined as visual stimuli in the AA subspace, the EE is formulated as a salient region detection problem, and the VD is automatically determined when there are no salient objects in the AA subspace. Since the spatial-contextual information of the endmembers is exploited during the saliency analysis, the proposed method is more robust than the spectral-only methods, which was verified using both real and synthetic hyperspectral images. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) is a crucial technique for exploiting remotely sensed hyperspectral data, which aims at estimating a set of spectral signatures, called endmembers and their corresponding proportions, called abundances. The performance of HU is often seriously degraded by various kinds of noise existing in hyperspectral images (HSIs). Most of existing robust HU methods are based on the assumption that noise or outlier only exists in one kind of formulation, e.g., band noise or pixel noise. However, in real-world applications, HSIs are unavoidably corrupted by noisy bands and noisy pixels simultaneously, which require robust HU in both the spatial dimension and spectral dimension. Meanwhile, the sparsity of abundances is an inherent property of HSIs and different regions in an HSI may possess various sparsity levels across locations. This article proposes a correntropy-based spatial-spectral robust sparsity-regularized unmixing model to achieve 2-D robustness and adaptive weighted sparsity constraint for abundances simultaneously. The updated rules of the proposed model are efficient to be implemented and carried out by a half-quadratic technique. The experimental results obtained by both synthetic and real hyperspectral data demonstrate the superiority of the proposed method compared to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) is an active research topic in the remote-sensing community. It aims at modeling mixed pixels using a collection of pure constituent materials (endmembers) weighted by their corresponding fractional abundances. Among existing unmixing schemes, nonnegative matrix factorization (NMF) has drawn significant attention due to its unsupervised nature, as well as its capacity to obtain both endmembers and fractional abundances simultaneously. In this article, we present a new blind unmixing method based on the generalized morphological component analysis (GMCA) framework, in which an additional constraint is introduced into the standard NMF model to represent the sparsity and morphological diversity of the abundance maps associated with each endmember. More specifically, we take into account the fact that different ground categories in a hyperspectral scene generally exhibit various spatial distributions and morphological characteristics. As a result, when providing a specific dictionary basis for these categories, their corresponding abundance maps (referred to as sources) can be sparsely represented. In addition, due to the low correlation between different sources, their sparse representations will not share the same most significant coefficients. With this observation in mind, we can further promote source discrimination and separation in the unmixing process. Moreover, in order to obtain a stable solution of the involved optimization problem, we adopt an alternate iterative constrained algorithm with a threshold descent strategy. Our experiments, carried out on both synthetic and real hyperspectral scenes, reveal that our newly developed GMCA-based unmixing method obtains very promising results with fast convergence speed and requiring significantly less parameter tuning. This confirms the advantage of the proposed spatial morphological component approach for HU purposes. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) is a crucial technique for exploiting remotely sensed hyperspectral data, which aims to estimate a set of spectral signatures, called endmembers and their corresponding proportions, called abundances. Nonnegative matrix factorization (NMF) and its various robust extensions have been widely applied to HU. Most existing robust NMF methods consider that noises only exist in one kind of formulation. However, the hyperspectral images (HSIs) are unavoidably corrupted by noisy bands and noisy pixels simultaneously in the real applications. This paper proposes a novel spectral–spatial robust NMF model by incorporating $\ell _{2,1}$ norm and $\ell _{1,2}$ norm, which achieves robustness to band noise and pixel noise simultaneously. The Huber’s M-estimator is integrated into the proposed model to achieve better assignations of weights for each pixel and band with various noise intensities, which avoids the singularity problem and effectively improves the unmixing performance. The elegant updating rules of the proposed spectral–spatial robust model are also efficiently learned and provided. Experiments are conducted on both synthetic and real hyperspectral data sets. The experimental results demonstrate the effectiveness of the proposed methods in unmixing performance. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) is an important task for remotely sensed hyperspectral (HS) data exploitation. It comprises the identification of pure spectral signatures (endmembers) and their corresponding fractional abundances in each pixel of the HS data cube. Several methods have been developed for (semi-) supervised and automatic identification of endmembers and abundances. Recently, the statistical dual-depth sparse probabilistic latent semantic analysis (DEpLSA) method has been developed to tackle the HU problem as a latent topic-based approach in which both endmembers and abundances can be simultaneously estimated according to the semantics encapsulated by the latent topic space. However, statistical models usually lead to computationally demanding algorithms and the computational time of the DEpLSA is often too high for practical use, in particular, when the dimensionality of the HS data cube is large. In order to mitigate this limitation, this article resorts to graphical processing units (GPUs) to provide a new parallel version of the DEpLSA, developed using the NVidia compute device unified architecture. Our experimental results, conducted using four well-known HS datasets and two different GPU architectures (GTX 1080 and Tesla P100), show that our parallel versions of the DEpLSA and the traditional pLSA approach can provide accurate HU results fast enough for practical use, accelerating the corresponding serial versions in at least 30x in the GTX 1080 and up to 147x in the Tesla P100 GPU, which are quite significant acceleration factors that increase with the image size, thus allowing for the possibility of the fast processing of massive HS data repositories. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for spectral unmixing of remotely sensed hyperspectral data. It exploits probabilistic latent topics in order to take advantage of the semantics pervading the latent topic space when identifying spectral signatures and estimating fractional abundances from hyperspectral images. Despite the contrasted potential of topic models to uncover image semantics, they have been merely used in hyperspectral unmixing as a straightforward data decomposition process. This limits their actual capabilities to provide semantic representations of the spectral data. The proposed model, called dual-depth sparse probabilistic latent semantic analysis (DEpLSA), makes use of two different levels of topics to exploit the semantic patterns extracted from the initial spectral space in order to relieve the ill-posed nature of the unmixing problem. In other words, DEpLSA defines a first level of deep topics to capture the semantic representations of the spectra, and a second level of restricted topics to estimate endmembers and abundances over this semantic space. An experimental comparison in conducted using the two standard topic models and the seven state-of-the-art unmixing methods available in the literature. Our experiments, conducted using four different hyperspectral images, reveal that the proposed approach is able to provide competitive advantages over available unmixing approaches. [ABSTRACT FROM AUTHOR]

In recent years, blind source separation (BSS) has received much attention in the hyperspectral unmixing field due to the fact that it allows the simultaneous estimation of both endmembers and fractional abundances. Although great performances can be obtained by the BSS-based unmixing methods, the decomposition results are still unstable and sensitive to noise. Motivated by the first law of geography, some recent studies have revealed that spatial information can lead to an improvement in the decomposition stability. In this paper, the group-structured prior information of hyperspectral images is incorporated into the nonnegative matrix factorization optimization, where the data are organized into spatial groups. Pixels within a local spatial group are expected to share the same sparse structure in the low-rank matrix (abundance). To fully exploit the group structure, image segmentation is introduced to generate the spatial groups. Instead of a predefined group with a regular shape (e.g., a cross or a square window), the spatial groups are adaptively represented by superpixels. Moreover, the spatial group structure and sparsity of the abundance are integrated as a modified mixed-norm regularization to exploit the shared sparse pattern, and to avoid the loss of spatial details within a spatial group. The experimental results obtained with both simulated and real hyperspectral data confirm the high efficiency and precision of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

Hyperspectral unmixing (HU) is one of the most active hyperspectral image (HSI) processing research fields, which aims to identify the materials and their corresponding proportions in each HSI pixel. The extensions of the nonnegative matrix factorization (NMF) have been proved effective for HU, which usually uses the sparsity of abundances and the correlation between the pixels to alleviate the non-convex problem. However, the commonly used L 1 / 2 sparse constraint will introduce an additional local minima because of the non-convexity, and the correlation between the pixels is not fully utilized because of the separation of the spatial and structural information. To overcome these limitations, a novel bilateral filter regularized L 2 sparse NMF is proposed for HU. Firstly, the L 2 -norm is utilized in order to improve the sparsity of the abundance matrix. Secondly, a bilateral filter regularizer is adopted so as to explore both the spatial information and the manifold structure of the abundance maps. In addition, NeNMF is used to solve the object function in order to improve the convergence rate. The results of the simulated and real data experiments have demonstrated the advantage of the proposed method.

Hyperspectral unmixing (HU) is one of the crucial steps for many hyperspectral applications, including material classification and recognition. In the last decade, non-negative matrix factorization (NMF) and its extensions have been widely studied and have achieved advanced performances in HU. Unfortunately, most of the existing NMF-based methods make the assumption that the hyperspectral data are only corrupted by Gaussian noise. In real applications, the hyperspectral data are inevitably corrupted by sparse noise, which includes impulse noise, stripes, deadlines, and others types of noise. By separately modeling the sparse noise and Gaussian noise, a robust NMF (RNMF) model is subsequently introduced to unmix the hyperspectral data. The proposed RNMF model is able to simultaneously handle Gaussian noise and sparse noise, and can be efficiently learned with elegant update rules. In addition, sparsity regularizers are added to restrict the abundance maps in the RNMF, with the consideration of the sparse property of the material types within the hyperspectral scene. The experimental results with simulated and real data confirm the superiority of the proposed sparsity-regularized RNMF methods compared to the traditional NMF methods. [ABSTRACT FROM PUBLISHER]

Hyperspectral image (HSI) unmixing has attracted increasing research interests in recent decades. The major difficulty of it lies in that the endmembers and the associated abundances need to be separated from highly mixed observation data with few a priori information. Recently, sparsity-constrained nonnegative matrix factorization (NMF) algorithms have been proved effective for hyperspectral unmixing (HU) since they can sufficiently utilize the sparsity property of HSIs. In order to improve the performance of NMF-based unmixing approaches, spectral and spatial constrains have been added into the unmixing model, but spectral–spatial joint structure is required to be more accurately estimated. To exploit the property that similar pixels within a small spatial neighborhood have higher possibility to share similar abundances, hypergraph structure is employed to capture the similarity relationship among the spatial nearby pixels. In the construction of a hypergraph, each pixel is taken as a vertex of the hypergraph, and each vertex with its $k$ nearest spatial neighboring pixels form a hyperedge. Using the hypergraph, the pixels with similar abundances can be accurately found, which enables the unmixing algorithm to obtain promising results. Experiments on synthetic data and real HSIs are conducted to investigate the performance of the proposed algorithm. The superiority of the proposed algorithm is demonstrated by comparing it with some state-of-the-art methods. [ABSTRACT FROM PUBLISHER]

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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. [ABSTRACT FROM PUBLISHER]

Abstract: Hyperspectral Unmixing (HU) has received increasing attention in the past decades due to its ability of unveiling information latent in hyperspectral data. Unfortunately, most existing methods fail to take advantage of the spatial information in data. To overcome this limitation, we propose a Structured Sparse regularized Nonnegative Matrix Factorization (SS-NMF) method based on the following two aspects. First, we incorporate a graph Laplacian to encode the manifold structures embedded in the hyperspectral data space. In this way, the highly similar neighboring pixels can be grouped together. Second, the lasso penalty is employed in SS-NMF for the fact that pixels in the same manifold structure are sparsely mixed by a common set of relevant bases. These two factors act as a new structured sparse constraint. With this constraint, our method can learn a compact space, where highly similar pixels are grouped to share correlated sparse representations. Experiments on real hyperspectral data sets with different noise levels demonstrate that our method outperforms the state-of-the-art methods significantly. [Copyright &y& Elsevier]

Hyperspectral endmember extraction is a process to estimate endmember signatures from the hyperspectral observations, in an attempt to study the underlying mineral composition of a landscape. However, estimating the number of endmembers, which is usually assumed to be known a priori in most endmember estimation algorithms (EEAs), still remains a challenging task. In this paper, assuming hyperspectral linear mixing model, we propose a hyperspectral data geometry-based approach for estimating the number of endmembers by utilizing successive endmember estimation strategy of an EEA. The approach is fulfilled by two novel algorithms, namely geometry-based estimation of number of endmembers—convex hull (GENE-CH) algorithm and affine hull (GENE-AH) algorithm. The GENE-CH and GENE-AH algorithms are based on the fact that all the observed pixel vectors lie in the convex hull and affine hull of the endmember signatures, respectively. The proposed GENE algorithms estimate the number of endmembers by using the Neyman–Pearson hypothesis testing over the endmember estimates provided by a successive EEA until the estimate of the number of endmembers is obtained. Since the estimation accuracies of the proposed GENE algorithms depend on the performance of the EEA used, a reliable, reproducible, and successive EEA, called p-norm-based pure pixel identification (TRI-P) algorithm is then proposed. The performance of the proposed TRI-P algorithm, and the estimation accuracies of the GENE algorithms are demonstrated through Monte Carlo simulations. Finally, the proposed GENE and TRI-P algorithms are applied to real AVIRIS hyperspectral data obtained over the Cuprite mining site, Nevada, and some conclusions and future directions are provided. [ABSTRACT FROM PUBLISHER]

Effective unmixing of hyperspectral data cube under a noisy scenario has been a challenging research problem in remote sensing arena. A branch of existing hyperspectral unmixing algorithms is based on Craig's criterion, which states that the vertices of the minimum-volume simplex enclosing the hyperspectral data should yield high fidelity estimates of the endmember signatures associated with the data cloud. Recently, we have developed a minimum-volume enclosing simplex (MVES) algorithm based on Craig's criterion and validated that the MVES algorithm is very useful to unmix highly mixed hyperspectral data. However, the presence of noise in the observations expands the actual data cloud, and as a consequence, the endmember estimates obtained by applying Craig-criterion-based algorithms to the noisy data may no longer be in close proximity to the true endmember signatures. In this paper, we propose a robust MVES (RMVES) algorithm that accounts for the noise effects in the observations by employing chance constraints. These chance constraints in turn control the volume of the resulting simplex. Under the Gaussian noise assumption, the chance-constrained MVES problem can be formulated into a deterministic nonlinear program. The problem can then be conveniently handled by alternating optimization, in which each subproblem involved is handled by using sequential quadratic programming solvers. The proposed RMVES is compared with several existing benchmark algorithms, including its predecessor, the MVES algorithm. Monte Carlo simulations and real hyperspectral data experiments are presented to demonstrate the efficacy of the proposed RMVES algorithm. [ABSTRACT FROM AUTHOR]