Unmixing Of Hyperspectral Images Research Articles

SUSHI: An algorithm for source separation of hyperspectralimages with non-stationary spectral variation. Semi-blind Unmixing with Sparsity for Hyperspectral Images

Hyperspectral images are data cubes with two spatial dimensions and a third spectral dimension, providing a spectrum for each pixel, and thus allowing the mapping of extended sources' physical properties. In this article, we present the Semi-blind Unmixing with Sparsity for Hyperspectral Images (SUSHI), an algorithm for non-stationary unmixing of hyperspectral images with spatial regularization of spectral parameters. The method allows for the disentangling of physical components without the assumption of a unique spectrum for each component. Thus, unlike most source separation methods used in astrophysics, all physical components obtained by SUSHI vary in spectral shape and in amplitude across the data cube. Non-stationary source separation is an ill-posed inverse problem that needs to be constrained. We achieve this by training a spectral model and applying a spatial regularization constraint on its parameters. For the spectral model, we used an Interpolatory Auto-Encoder, a generative model that can be trained with limited samples. For spatial regularization, we applied a sparsity constraint on the wavelet transform of the model parameter maps. We applied SUSHI to a toy model meant to resemble supernova remnants in X-ray astrophysics, though the method may be used on any extended source with any hyperspectral instrument. We compared this result to the one obtained by a classic 1D fit on each individual pixel. We find that SUSHI obtains more accurate results, particularly when it comes to reconstructing physical parameters. We then applied SUSHI to real X-ray data from the supernova remnant Cassiopeia A and to the Crab Nebula. The results obtained are realistic and in accordance with past findings but have a much better spatial resolution. Thanks to spatial regularization, SUSHI can obtain reliable physical parameters at fine scales that are out of reach for pixel-by-pixel methods.

Deep Attention-Guided Spatial–Spectral Network for Hyperspectral Image Unmixing

Deep Attention-Guided Spatial–Spectral Network for Hyperspectral Image Unmixing

Robust Dual Spatial Weighted Sparse Unmixing for Remotely Sensed Hyperspectral Imagery

Sparse unmixing plays a crucial role in the field of hyperspectral image unmixing technology, leveraging the availability of pre-existing endmember spectral libraries. In recent years, there has been a growing trend in incorporating spatial information from hyperspectral images into sparse unmixing models. There is a strong spatial correlation between pixels in hyperspectral images (that is, the spatial information is very rich), and many sparse unmixing algorithms take advantage of this to improve the sparse unmixing effect. Since hyperspectral images are susceptible to noise, the feature separability of ground objects is reduced, which makes most sparse unmixing methods and models face the risk of degradation or even failure. To address this challenge, a novel robust dual spatial weighted sparse unmixing algorithm (RDSWSU) has been proposed for hyperspectral image unmixing. This algorithm effectively utilizes the spatial information present in the hyperspectral images to mitigate the impact of noise during the unmixing process. For the proposed RDSWSU algorithm, which is based on ℓ1 sparse unmixing framework, a pre-calculated superpixel spatial weighting factor is used to smooth the noise, so as to maintain the original spatial structure of hyperspectral images. The RDSWSU algorithm, which builds upon the ℓ1 sparse unmixing framework, employs a pre-calculated spatial weighting factor at the superpixel level. This factor aids in noise smoothing and helps preserve the inherent spatial structure of hyperspectral images throughout the unmixing process. Additionally, another spatial weighting factor is utilized in the RDSWSU algorithm to capture the local smoothness of abundance maps at the sub-region level. This factor helps enhance the representation of piecewise smooth variations within different regions of the hyperspectral image. Specifically, the combination of these two spatial weighting factors in the RDSWSU algorithm results in an enhanced sparsity of the abundance matrix. The RDSWSU algorithm, which is a sparse unmixing model, offers an effective solution using the alternating direction method of multiplier (ADMM) with reduced requirements for tuning the regularization parameter. The proposed RDSWSU method outperforms other advanced sparse unmixing algorithms in terms of unmixing performance, as demonstrated by the experimental results on synthetic and real hyperspectral datasets.

Smoothed separable nonnegative matrix factorization

Given a set of data points belonging to the convex hull of a set of vertices, a key problem in linear algebra, signal processing, data analysis and machine learning is to estimate these vertices in the presence of noise. Many algorithms have been developed under the assumption that there is at least one nearby data point to each vertex; two of the most widely used ones are vertex component analysis (VCA) and the successive projection algorithm (SPA). This assumption is known as the pure-pixel assumption in blind hyperspectral unmixing, and as the separability assumption in nonnegative matrix factorization. More recently, Bhattacharyya and Kannan (ACM-SIAM Symposium on Discrete Algorithms, 2020) proposed an algorithm for learning a latent simplex (ALLS) that relies on the assumption that there is more than one nearby data point to each vertex. In that scenario, ALLS is probabilistically more robust to noise than algorithms based on the separability assumption. In this paper, inspired by ALLS, we propose smoothed VCA (SVCA) and smoothed SPA (SSPA) that generalize VCA and SPA by assuming the presence of several nearby data points to each vertex. We illustrate the effectiveness of SVCA and SSPA over VCA, SPA and ALLS on synthetic data sets, on the unmixing of hyperspectral images, and on feature extraction on facial images data sets. In addition, our study highlights new theoretical results for VCA.

Local spatial similarity based joint-sparse regression for hyperspectral image unmixing

Hyperspectral unmixing is indispensable for hyperspectral remote sensing technology. Exploration of spatial and spectral information helps to obtain accurate abundances. In recent years, utilizing a joint-sparse prior of the abundance matrix has earned a lot of interest. The joint-sparse-blocks structure considers the joint sparsity among column blocks (neighboring pixels) of an abundance matrix. Considering different ways of tensor expansion, the bilateral joint-sparse structure is extended to consider the joint sparsity along both horizontal and vertical directions. But it is still hard to fully utilize spectral and spatial information in hyperspectral data. In this article, we propose a local spatial similarity based joint-sparse structure by imposing the joint sparse on similar pixels in a local region, instead of only horizontally and vertically adjacent pixels. Specifically, we assume that similar pixels share identical endmembers. In this vein, we enhance the sparsity of local related pixels and have a deeper mining of the spatial information in hyperspectral data. Moreover, combined with a low-rank property, we propose a new unmixing model and derive an algorithm under the alternating direction method of multipliers framework. The validity of the proposed algorithm is verified by experiments on both synthetic and real data, compared with several state-of-the-art unmixing algorithms.

Spectral unmixing of hyperspectral images based on block sparse structure

Spectral unmixing of hyperspectral images based on block sparse structure

Integration of Physics-Based and Data-Driven Models for Hyperspectral Image Unmixing: A summary of current methods

Spectral unmixing is one of the most important quantitative analysis tasks in hyperspectral data processing. Conventional physics-based models are characterized by clear interpretation. However they may not be suitable for analyzing scenes with unknown complex physical characteristics. Data-driven methods have developed rapidly in recent years, in particular deep learning methods because they possess superior capability in modeling complex and nonlinear systems. Simply transferring these methods as black-boxes to conduct unmixing may lead to low physical interpretability and generalization ability. This article reviews hyperspectral unmixing works that integrate advantages of both physics-based models and data-driven methods by means of deep neural network structures design, prior design and loss design. Most of these methods derive from a common mathematical optimization framework, and combine good interpretability with high accuracy.

Graph learning and denoising-based weighted sparse unmixing for hyperspectral images

ABSTRACT Sparse unmixing is a semisupervised unmixing method based on the linear mixture model, in which the spectral library is known a prior, and has received considerable attention recently. It has been confirmed that the spatial information in hyperspectral images plays a crucial role in improving the performance of sparse unmixing algorithms. However, the spatial information extracted or captured in most unmixing algorithms is inaccurate and robust enough, which leads to artificial block noise or outliers in the estimated abundance maps, especially as the noise level increases. To address these problems and more efficiently utilize the spatial information, this paper proposes a graph learning and denoising-based weighted sparse mixing (GLDWSU) algorithm, which includes three stages in the unmixing procedure: graph learning, denoising and unmixing. In the first stage, the graph Laplacian matrix is adaptively learned to capture the spatial structure of HSI with the relative total variation (RTV) regularization. In the next stage, HSI is denoised with the learned Laplacian matrix by using Laplacian smoothing. In the final stage, the denoised HSI is unmixed with the reweighted-norm regularization based on the alternating direction method of multipliers (ADMM) framework. The experimental results on both simulated and real data sets show that the proposed GLDWSU algorithm can more accurately capture and utilize the spatial structure information of HSI with a low computational cost and outperforms all the compared methods.

Intrinsic Decomposition Embedded Spectral Unmixing for Satellite Hyperspectral Images With Endmembers From UAV Platform

Intrinsic Decomposition Embedded Spectral Unmixing for Satellite Hyperspectral Images With Endmembers From UAV Platform

Local Spectral Similarity-Guided Sparse Unmixing of Hyperspectral Images With Spatial Graph Regularization

Local Spectral Similarity-Guided Sparse Unmixing of Hyperspectral Images With Spatial Graph Regularization

Adaptive multiscale sparse unmixing for hyperspectral remote sensing image

Sparse unmixing of hyperspectral images aims to separate the endmembers and estimate the abundances of mixed pixels. This approach is the essential step for many applications involving hyperspectral images. The multi-scale spatial sparse hyperspectral unmixing algorithm (MUA) could achieve higher accuracy than many state-of-the-art algorithms. The regularization parameters, whose combinations markedly influence the unmixing accuracy, are determined by manually searching in the broad parameter space, leading to time consuming. To settle this issue, the adaptive multi-scale spatial sparse hyperspectral unmixing algorithm (AMUA) is proposed. Firstly, the MUA model is converted into a new version by using of a maximum a posteriori (MAP) system. Secondly, the theories indicating that andnorms are equivalent to Laplacian and multivariate Gaussian functions, respectively, are applied to explore the strong connections among the regularization parameters, estimated abundances and estimated noise variances. Finally, the connections are applied to update the regularization parameters adaptively in the optimization process of unmixing. Experimental results on both simulated data and real hyperspectral images show that the AMUA can substantially improve the unmixing efficiency at the cost of negligible accuracy. And a series of sensitive experiments were undertook to verify the robustness of the AMUA algorithm.

Spectral weighted sparse unmixing of hyperspectral images based on framelet transform

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Multiview Spatial–Spectral Two-Stream Network for Hyperspectral Image Unmixing

Linear spectral unmixing is an important technique in the analysis of mixed pixels in hyperspectral images. In recent years, deep learning-based methods have been garnering increasing attention in hyperspectral unmixing; especially, unsupervised autoencoder (AE) networks that have achieved excellent unmixing performance are a recent trend. While most approaches use spatial information, it is well known that hyperspectral data are characterized by a large number of narrow spectral bands. In order to take full advantage of the hyperspectral bands in unmixing and the spatial information, in this article, we explore multiview spectral and spatial information in an AE-based unmixing framework. We introduce multiview spectral information through spectral partitioning and propose a multiview spatial–spectral two-stream network, called MSSS-Net, which simultaneously learns a spatial stream network and a multiview spectral stream network in an end-to-end fashion for more efficient unmixing. The MSSS-Net is a two-stream deep unmixing network sharing a decoder, where its two AE networks employ recurrent neural networks (RNNs) to collaboratively utilize multiview spectral and spatial information. The spatial stream network branch extracts the spatial features of pixels and its neighbors, while the multiview spectral stream network branch exploits the multiview spectral bands of a pixel. Meanwhile, we design a cascaded bidirectional and unidirectional RNNs’ encoder structure for multiview spatial–spectral information to learn more discriminative deep patch-pixel features. Extensive ablation studies and experiments on both synthetic and real datasets demonstrate the superiority of the MSSS-Net over state-of-the-art unmixing methods.

Endmember Bundle Extraction Based on Improved Multiobjective Particle Swarm Optimization

Endmember extraction (EE) is a key task for hyperspectral image 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 paper proposes an improved multi-objective 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 multi-objective 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 endmember bundle extraction 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.

Nonlinear extended blind end-member and abundance extraction for hyperspectral images

Hyperspectral images had become an essential tool in different application frameworks, such as mineral exploration, food inspection, and medical assessment, among others. However, the interpretability of these images involves an initial processing stage to model the optical interaction and analyze the spectral information. In this work, we study nonlinear unmixing of hyperspectral images by a multilinear mixture model (MMM). In this sense, we propose a nonlinear version of the extended blind end-member and abundance extraction (NEBEAE) method for blind unmixing, i.e. estimation of the end-members, their abundances, and the nonlinear interaction levels. In the problem formulation, we include a normalization step in the hyperspectral measurements for the end-members and abundances to improve robustness. The blind unmixing process can be separated into three estimation subproblems for each component in the model, which are solved by a cyclic coordinate descent algorithm and quadratic constrained optimizations. Each problem is mathematically formulated and derived to construct the general nonlinear iterative unmixing technique. We evaluated our proposal with synthetic and experimental datasets from the remote sensing literature (Cuprite, Urban and Pavia University scene datasets) and a biomedical hyperspectral imaging application. In the validation stage, we compared NEBEAE with three state-of-the-art methods to show its advantages in terms of precision and computational time.

Refinement of Hottopixx Method for Nonnegative Matrix Factorization Under Noisy Separability

Hottopixx, proposed by Bittorf et al. at NIPS 2012, is an algorithm for solving nonnegative matrix factorization (NMF) problems under the separability assumption. Separable NMFs have important applications, such as topic extraction from documents and unmixing of hyperspectral images. In such applications, the robustness of the algorithm to noise is the key to success. Hottopixx has been shown to be robust to noise, and its robustness can be further enhanced through postprocessing. However, there is a drawback. Hottopixx and its postprocessing require us to estimate the noise level involved in the matrix we want to factorize before running, since they use it as part of the input data. The noise-level estimation is not an easy task. In this paper, we overcome this drawback. We present a refinement of Hottopixx and its postprocessing that runs without prior knowledge of the noise level. We show that the refinement has almost the same robustness to noise as the original algorithm.

Robust generalized bilinear model with weighted low-rank representation for hyperspectral image unmixing

The generalized bilinear model (GBM) has been one of the most representative models for nonlinear unmixing of hyperspectral images (HSI), which can consider the second-order scattering of photons. Recently, robust GBM-low-rank representation (RGBM-LRR) for nonlinear unmixing of HSI has been introduced to capture the spatial correlation of HSI using LRR with nuclear norm minimization (NNM). However, NNM is used to approximate the matrix rank by shrinkage all singular values equally. The singular values have distinct physical significance in many real applications, and NNM may not be able to estimate the matrix rank accurately. To overcome the above issue, a robust GBM with a weighted low-rank representation (RGBM-WLRR) approach is proposed using weighted nuclear norm minimization, which mitigates the penalty on larger singular values by assigning a small weight, so the corresponding shrinkage is small and also takes serious shrinkage on small singular values by assigning larger weights to them. The proposed model is solved using an iterative alternating direction method of the multipliers. A series of experiments with real datasets and a simulated HSI with varying rank and signal-to-noise ratio reveals that RGBM-WLRR performs significantly better than the state-of-the-art algorithms in terms of signal-to-reconstruction error, root-mean-square error, and spectral angle distance.

Assessment of spectral reduction techniques for endmember extraction in unmixing of hyperspectral images

Spectral mixture modelling is one of the most important techniques for classifying hyperspectral data at sub-pixel resolution. The identification of spectrally pure endmembers for estimating their corresponding abundances is an important step in spectral unmixing. The application of spectral reduction prior to endmember extraction would optimize the process by increasing the sensitivity of the algorithms to the most distinctive and informative features of the dataset. The objective of this study is to compare different spectral reduction techniques prior to endmember extraction on six real hyperspectral datasets, including an Airborne Visible InfraRed Imaging Spectrometer- Next Generation (AVIRIS-NG) image over Indian sub-continent. The endmembers identified from different combinations of spectral reduction and endmember extraction techniques are used for linear spectral unmixing on the original datasets. The performance of such combinations after unmixing were compared in terms of pixel reconstruction error and also the computation time for each dataset. Spectral reduction by both feature extraction techniques like Principal Component Analysis (PCA), Independent Component Analysis (ICA), Minimum Noise Fraction (MNF), and a feature selection technique based on Partial Informational Correlation (PIC) measure were analysed. The PIC based spectral reduction was found to perform well in terms of reconstruction error and computation time when combined with N-FINDR endmember algorithm. This approach could be adopted for spectral reduction in unmixing of datasets with similar endmember classes.

Combining low-rank constraint for similar superpixels and total variation sparse unmixing for hyperspectral image

ABSTRACT Mixed pixels are the main reason for the low accuracy of traditional remote sensing applications. Hyperspectral image unmixing can explore the sub-pixel information of mixed pixels, which is an effective measure to solve the problems of low precision. Current unmixing methods only consider the correlation of local or global pixels and do not fully utilize images information. Based on the above problems, we proposed a novel sparse unmixing model named combining low-rank constrain for similar superpixels and total variation sparse unmixing (CLRSS-TV) in this current research paper. The adjacent similar pixels are clustered first into superpixels, then the superpixels with the same semantic information are merged into a collection. The spatial information of the image is fully considered by twice clustering. Weighted low-rank constraint is imposed on each collection to consider the spectral correlation of pixels. Moreover, the TV regularization and l 2,1 norm are utilized to improve the smoothness and row sparsity, respectively. Experimental results reveal that the proposed method is not only competitive with the four state-of-the-art algorithms in simulated and actual datasets, but also has good anti-noise ability and universality. However, this paper still fails to overcome the problem of parameters selection in sparse unmixing, so the future work study intends to adopt the intelligent optimization algorithm to obtain the optimal parameters.

SISAL Revisited

Simplex identification via split augmented Lagrangian (SISAL) is a popularly used algorithm in blind unmixing of hyperspectral images. Developed by José M. Bioucas-Dias in 2009, the algorithm is fundamentally relevant to tackling simplex-structured matrix factorization and, by extension, nonnegative matrix factorization, which have many applications under their umbrellas. In this article, we revisit SISAL and provide new meanings to this quintessential algorithm. The formulation of SISAL was motivated from a geometric perspective, with no noise. We show that SISAL can be explained as an approximation scheme from a probabilistic simplex component analysis framework, which is statistical and is principally more powerful in accommodating the presence of noise. The algorithm for SISAL was designed based on a successive convex approximation method, with a focus on practical utility. It was not known, by analyses, whether the SISAL algorithm has any kind of guarantee of convergence to a stationary point. By establishing associations between the SISAL algorithm and a line search--based proximal gradient method, we confirm that SISAL can indeed guarantee convergence to a stationary point. Our re-explanation of SISAL also reveals new formulations and algorithms. The performance of these new possibilities is demonstrated by numerical experiments.