Simultaneously Sparse and Low-Rank Abundance Matrix Estimation for Hyperspectral Image Unmixing

Abstract

In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time. This premise has recently guided the research to the innovative and meaningful idea of imposing multiple constraints on the unknown parameters involved in the problem under study. For instance, when dealing with problems whose unknown parameters form sparse and low-rank matrices, the adoption of suitably combined constraints imposing sparsity and lowrankness, is expected to yield substantially enhanced estimation results. In this paper, we address the spectral unmixing problem in hyperspectral images. Specifically, two novel unmixing algorithms are introduced, in an attempt to exploit both spatial correlation and sparse representation of pixels lying in homogeneous regions of hyperspectral images. To this end, a novel mixed penalty term is first defined consisting of the sum of the weighted 1 and the weighted nuclear norm of the abundance matrix corresponding to a small area of the image determined by a sliding square window. This penalty term is then used to regularize a conventional quadratic cost function and impose simultaneously sparsity and row-rankness on the abundance matrix. The resulting regularized cost function is minimized by a) an incremental proximal sparse and low-rank unmixing algorithm and b) an algorithm based on the alternating minimization method of multipliers (ADMM). The effectiveness of the proposed algorithms is illustrated in experiments conducted both on simulated and real data. Index TermsSemi-supervised spectral unmixing, hyperspectral images, simultaneously sparse and low-rank matrices, proximal methods, alternating direction method of multipliers (ADMM), abundance estimation

Joint Local Abundance Sparse Unmixing for Hyperspectral Images

“…In a physical sense, the pixels in such regions contain the same materials, either in the same or different fractions. Hence, the abundance matrix of the region can be estimated by the low-rank property [30,34].…”

“…We evaluated the results by conducting a fair comparison with the CLSUnSAL [28] and SunSAL-TV [27]. State-of-the-art low-rank algorithm is also compared, which is sparse and low-rank unmixing by using ADMM (ADSpLRU) [34].…”

“…The parameter settings of J-LASU are for the collaborative sparsity (λ), TV (γ), and LA nuclear norm (ρ) regularizer. For the compared algorithms, λ SP is the sparsity term for CLSUnSAL, SUnSAL-TV, and ADSpLRU [34]. For SUnSAL-TV, the TV term is controlled by λ TV .…”

“…Furthermore, the low-rankness of the data also indicates high correlation among the abundance vectors corresponding to the pixels in such regions [30]. Giampouras et al [34] proposed ADSpLRU algorithm by exploiting the low-rankness of abundance to the sparse unmixing problem to consider the spatial correlation of the abundance. However, they considered the low-rankness in the nonlocal fashion of the abundance dimension.…”

Retrieval of Mineral Abundances of the Delta Region in Eberswalde, Mars

“…Sparse unmixing is an active research area in hyperspectral unmixing in recent years (Giampouras et al, 2015;Iordache et al, 2011Iordache et al, , 2012Iordache et al, , 2014aIordache et al, 2014b;Shi et al, 2014;Tang et al, 2015), which aims to find the optimal subset of signatures in a spectral library that can best model hyperspectral data. A sparsity regularizer is commonly imposed to promote the number of selected signatures as small as possible.…”