Sparse Unmixing Approaches Research Articles

Spectral weighted sparse unmixing based on adaptive total variation and low-rank constraints

Hyperspectral sparse unmixing, an image processing technique, leverages a spectral library enriched with endmember spectral information as a prerequisite. It decomposes the hyperspectral data to ascertain the abundance corresponding to each endmember in the spectral library. Currently, the majority of sparse unmixing methods are inadequate in high-noise environments due to their failure to comprehensively account for hyperspectral characteristics. Addressing this challenge, this paper introduces an innovative sparse unmixing approach for hyperspectral images named spectral weighted sparse unmixing based on adaptive total variation and low-rank constraints (SWSU-ATVLR). Initially, the sparse unmixing algorithm is introduced in detail. Subsequently, we present the our method. This method seamlessly integrates the low-rank, adaptive TV and spectral weighting characteristics of hyperspectral data. While preserving the low-rank attributes and sparsity of abundance, the adaptively adjusted abundance matrix exhibits a regularized horizontal and vertical difference ratio across various structures and fully utilizes spectral information, enhancing denoising efficiency. Subsequently, the ADMM algorithm is employed to solve the new model. To validate our proposed algorithm, SWSU-ATVLR method is compared and analysed in detailed experiments with several current state-of-the-art methods through simulated and real data experiments. Experimental results prove that our proposed method is superior to these state-of-the-art methods.

Multiobjective sparse unmixing based hyperspectral change detection

Hyperspectral unmixing can provide the composition of ground objects, while change detection can identify the changes of the same region over time. Therefore, unmixing based hyperspectral change detection can investigate changes in a subpixel-level. It can provide not only whether the change happens or not but also how to change. This paper will gradually establish an unconstrained sparse unmixing based change detection model and design a multiobjective optimization sparse unmixing approach (termed MoSU-CD) to solve it for more subpixel-level change details. Compared with the existing sparse unmixing based change detection approaches, MoSU-CD directly unmixes the difference map of multi-temporal images rather than multi-temporal images themselves respectively. Then it explores the change details of one substance in each pixel based on the unmixing results, i.e., endmembers and abundances. In addition, in order to improve the change detection accuracy, an ensemble decision strategy is designed for the Pareto optimal solutions obtained by multiobjective optimization method. Based on this strategy, the subpixel-level changes can be aggregated to generate an aggressive pixel-level change map. The experimental results on synthetic and real data sets demonstrate that the proposed MoSU-CD not only outperforms the benchmark and state-of-art approaches in terms of pixel-level change detection but also provides additional subpixel-level change information.

Structured low-rank representation learning for hyperspectral sparse unmixing

ABSTRACT Sparse unmixing methods have been widely used to estimate the abundance of each material component from hyperspectral images. However, conventional sparse unmixing approaches only consider matrix factorization without limited explorations on the high-dimensional structures of the third-order tensors. To address this issue, we propose SUnSLRR, a novel approach to sparse unmixing of hyperspectral data based on structured low-rank tensor modelling. In contrast to traditional methods, SUnSLRR leverages the low-rank property underlying the abundance tensor to exploit structural details from multiple modes. By incorporating sparsity regularization and a low-rank constraint, SUnSLRR can effectively extract the intrinsic features of hyperspectral data. We apply the alternating direction method of multipliers framework to solve the optimization problem induced by SUnSLRR, and experiments conducted on simulated and real hyperspectral images demonstrate the superior effectiveness of our proposed method compared to traditional methods in terms of both accuracy and efficiency.

Superpixel-Based Weighted Collaborative Sparse Regression and Reweighted Low-Rank Representation for Hyperspectral Image Unmixing

Sparse unmixing with a semisupervised fashion has been applied to hyperspectral remote sensing imagery. However, the imprecise spatial contextual information, the lack of global feature and the high mutual coherences of a spectral library greatly limit the performance of sparse unmixing. In order to address these prominent problems, a new paradigm to characterize sparse hyperspectral unmixing is proposed, namely, the superpixel-based weighted collaborative sparse regression and reweighted low-rank representation unmixing (SBWCRLRU). In this method, the weighted collaborative sparse regression explores the pixels shared the same support set to help the sparsity of abundance fraction, and the reweighted low rank representation minimizes the rank of the abundance matrix to promote the spatial consistency of the image. Meanwhile, superpixel segmentation is adopted to cluster the pixels into different spatial homogeneous regions to further improve the unmixing performance. Extensive experiments results conducted on both synthetic and real data demonstrate the effectiveness of the proposed SBWCRLRU. It can not only improve the performance of hyperspectral unmixing but also outperform the existing sparse unmixing approaches.

Superpixel-Based Reweighted Low-Rank and Total Variation Sparse Unmixing for Hyperspectral Remote Sensing Imagery

Sparse unmixing, as a semisupervised unmixing method, has attracted extensive attention. The process of sparse unmixing involves treating the mixed pixels of hyperspectral imagery as a linear combination of a small number of spectral signatures (endmembers) in a standard spectral library, associated with fractional abundances. Over the past ten years, to achieve a better performance, sparse unmixing algorithms have begun to focus on the spatial information of hyperspectral images. However, less accurate spatial information greatly limits the performance of the spatial-regularization-based sparse unmixing algorithms. In this article, to overcome this limitation and obtain more reliable spatial information, a novel sparse unmixing algorithm named superpixel-based reweighted low-rank and total variation (SUSRLR-TV) is proposed to enhance the performance of the traditional spatial-regularization-based sparse unmixing approaches. In the proposed approach, superpixel segmentation is adopted to consider both the spatial proximity and the spectral similarity. In addition, a low-rank constraint is enforced on the objective function as pixels within each superpixel have the same endmembers and similar abundance values, and they naturally satisfy the low-rank constraint. Differing from the traditional nuclear norm, a reweighted nuclear norm is used to achieve a more efficient and accurate low-rank constraint. Meanwhile, low-rank consideration is also used to enhance the spatial continuity and suppress the effects of random noise. Furthermore, TV regularization is introduced to promote the smoothness of the abundance maps. Experiments on three simulated data sets, as well as a well-known real hyperspectral imagery data set, confirm the superior performance of the proposed method in both the qualitative assessment and the quantitative evaluation, compared with the state-of-the-art sparse unmixing methods.

Rolling Guidance Based Scale-Aware Spatial Sparse Unmixing for Hyperspectral Remote Sensing Imagery

Spatial regularization based sparse unmixing has attracted much attention in the hyperspectral remote sensing image processing field, which combines spatial information consideration with a sparse unmixing model, and has achieved improved fractional abundance results. However, the traditional spatial sparse unmixing approaches can suppress discrete wrong unmixing points and smooth an abundance map with low-contrast changes, and it has no concept of scale difference. In this paper, to better extract the different levels of spatial details, rolling guidance based scale-aware spatial sparse unmixing (namely, Rolling Guidance Sparse Unmixing (RGSU)) is proposed to extract and recover the different levels of important structures and details in the hyperspectral remote sensing image unmixing procedure, as the different levels of structures and edges in remote sensing imagery have different meanings and importance. Differing from the existing spatial regularization based sparse unmixing approaches, the proposed method considers the different levels of edges by combining a Gaussian filter-like method to realize small-scale structure removal with a joint bilateral filtering process to account for the spatial domain and range domain correlations. The proposed method is based on rolling guidance spatial regularization in a traditional spatial regularization sparse unmixing framework, and it accomplishes scale-aware sparse unmixing. The experimental results obtained with both simulated and real hyperspectral images show that the proposed method achieves visual effects better and produces higher quantitative results (i.e., higher SRE values) when compared to the current state-of-the-art sparse unmixing algorithms, which illustrates the effectiveness of the rolling guidance based scale aware method. In the future work, adaptive scale-aware spatial sparse unmixing framework will be studied and developed to enhance the current idea.

Semisupervised Endmember Identification in Nonlinear Spectral Mixtures via Semantic Representation

This paper proposes a new hyperspectral unmixing method for nonlinearly mixed hyperspectral data using a semantic representation in a semi-supervised fashion, assuming the availability of a spectral reference library. Existing semi-supervised unmixing algorithms select members from an endmember library that are present at each of the pixels; most such methods assume a linear mixing model. However, those methods will fail in the presence of nonlinear mixing among the observed spectra. To address this issue, we develop an endmember selection method using a recently proposed semantic spectral representation obtained via non-homogeneous hidden Markov chain (NHMC) model for a wavelet transform of the spectra. The semantic representation can encode spectrally discriminative features for any observed spectrum and, therefore, our proposed method can perform endmember selection without any assumption on the mixing model. Experimental results show that in the presence of sufficiently nonlinear mixing our proposed method outperforms dictionary-based sparse unmixing approaches based on linear models.

Reweighted Sparse Regression for Hyperspectral Unmixing

Hyperspectral unmixing (HSU) plays an important role in hyperspectral image (HSI) analysis. Recently, the HSU method based on sparse regression has drawn much attention. This paper presents a new weighted sparse regression problem for HSU and proposes two iterative reweighted algorithms for solving this problem, where the weights used for the next iteration are computed from the value of the current solution, and all the mixed pixels of an HSI are unmixed simultaneously. The proposed algorithms can be seen as the combinations of alternating direction method of multipliers and iterative reweighting procedure. Experimental results on both synthetic and real data demonstrate some advantages of the proposed algorithms over some other state-of-the-art sparse unmixing approaches.

Equivalent-Sparse Unmixing Through Spatial and Spectral Constrained Endmember Selection From an Image-Derived Spectral Library

Spectral variation, which is inevitably present in hyperspectral data due to nonuniformity and inconsistency of illumination, may result in considerable difficulty in spectral unmixing. In this paper, a field endmember library is constructed to accommodate spectral variation by representing each endmember class by a batch of image-derived spectra. In order to perform unmixing by such a field endmember library, a novel spatial and spectral endmember selection (SSES) algorithm is designed to search for a spatial and spectral constrained endmember subset per pixel for abundance estimation (AE). The net effect is to achieve sparse unmixing equivalently, considering the fact that only a few endmembers in the large library have nonzero abundances. Thus, the resulting algorithm is called spatial and spectral constrained sparse unmixing (SSCSU). Experimental results using both synthetic and real hyperspectral images demonstrate that the proposed SSCSU algorithm not only improves the performance of traditional AE algorithms by considering spectral variation, but also outperforms the existing sparse unmixing approaches.

When Pixels Team up: Spatially Weighted Sparse Coding for Hyperspectral Image Classification

In this letter, a spatially weighted sparse unmixing approach is proposed as a front-end for hyperspectral image classification using a linear SVM. The idea is to partition the pixels of a hyperspectral image into a number of disjoint spatial neighborhoods. Since neighboring pixels are often composed of similar materials, their sparse codes are encouraged to have similar sparsity patterns. This is accomplished by means of a reweighted ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> framework where it is assumed that fractional abundances of neighboring pixels are distributed according to a common Laplacian Scale Mixture (LSM) prior with a shared scale parameter. This shared parameter determines which endmembers contribute to the group of pixels. Experiments on the AVIRIS Indian Pines show that the model is very effective in finding discriminative representations for HSI pixels, especially when the training data is limited.

Hyperspectral image unmixing using a sparse Bayesian model

Hyperspectral unmixing is a technique that can be used to find the materials and their corresponding proportions present in observed mixed pixels. It has been widely used for hyperspectral data exploitation. Traditionally, this problem is solved using the constrained least squares optimization, which would lead to a dense solution. In recent years, researchers have observed that the number of materials in a mixed pixel is generally much smaller than the whole number of materials present in a given scene. They proposed to solve the problem through sparse unmixing approaches, which generally lead to constrained optimization. These sparse unmixing approaches have received considerable attention over the past few years. From the perspective of Bayesian inference, these methods assume fixed priors. In this article, we propose to solve the spectral unmixing problem by using sparse Bayesian learning (SBL) framework. In contrast to the approaches that use fixed priors, SBL incorporates a hierarchical parameterized prior that encourages sparsity in representation in its Bayesian inference to obtain a sparse solution. Experimental results on simulated data sets and a real hyperspectral scene demonstrate that the proposed method can achieve good performance compared with some state-of-the-art sparse unmixing algorithms. Our results also show that the proposed method can achieve good performance with a set of default parameter settings.