MUSIC-CSR: Hyperspectral Unmixing via Multiple Signal Classification and Collaborative Sparse Regression

Abstract

Spectral unmixing aims at finding the spectrally pure constituent materials (also called endmembers) and their respective fractional abundances in each pixel of a hyperspectral image scene. In recent years, sparse unmixing has been widely used as a reliable spectral unmixing methodology. In this approach, the observed spectral vectors are expressed as linear combinations of spectral signatures assumed to be known a priori and present in a large collection, termed spectral library or dictionary, usually acquired in laboratory. Sparse unmixing has attracted much attention as it sidesteps two common limitations of classic spectral unmixing approaches: the lack of pure pixels in hyperspectral scenes and the need to estimate the number of endmembers in a given scene, which are very difficult tasks. However, the high mutual coherence of spectral libraries, jointly with their ever-growing dimensionality, strongly limits the operational applicability of sparse unmixing. In this paper, we introduce a two-step algorithm aimed at mitigating the aforementioned limitations. The algorithm exploits the usual low dimensionality of the hyperspectral data sets. The first step, similar to the multiple signal classification (MUSIC) array signal processing algorithm, identifies a subset of the library elements which contains the endmember signatures. Because this subset has cardinality much smaller than the initial number of library elements, the sparse regression we are led to is much more well-conditioned than the initial one using the complete library. The second step applies collaborative sparse regression (CSR), which is a form of structured sparse regression, exploiting the fact that only a few spectral signatures in the library are active.The effectiveness of the proposed approach, termed MUSIC-CSR, is extensively validated using both simulated and real hyperspectral data sets. Index TermsHyperspectral imaging, hyperspectral unmixing, spectral libraries, sparse unmixing, sparse regression, collaborative sparse regression, dictionary pruning, MUSIC, array signal processing.

A Novel Spectral Library Pruning Technique for Spectral Unmixing of Urban Land Cover

“…The algorithm does so by representing the original image as a small set of eigenvectors and subsequently calculating the distance from each library entry to this simplified representation. MUSIC-PA has already been successfully applied on both simulated and real hyperspectral datasets of mainly semi-natural environments (i.e., citrus orchards) and has been shown to increase the accuracy and computational efficiency of subpixel fraction mapping using sparse unmixing [9]. However, during our first experiences with MUSIC-PA in more complex, urban environments we identified remaining redundancies in the final spectral libraries and revealed potential room for improvement [31].…”

“…Unlike IES, MUSIC-PA [9] is an image-based library pruning method designed to select, from a large library, a subset of pure spectra that best represents the spectral variability of a given hyperspectral image and that, as a consequence, constitutes the best input for subpixel fractional abundance estimation. MUSIC-PA essentially comprises two steps.…”

“…As the quality of the spectral library is key to the success of the unmixing procedure [4], this initial library is often further optimized, i.e., a library subset is selected that optimally represents the endmember variability in the specific image to be processed. This library pruning step has been shown to increase both the computational efficiency (less spectra to be processed) and the accuracy (less spectral confusion) of the subsequent unmixing analysis [9,10].…”

“…Given the size of a generic spectral library, in combination with the high number of pixels within (especially high resolution) imagery, adopting a pixel-wise library pruning strategy may prove to be computationally inefficient. The MUSIC pruning algorithm (referred hereinafter as "MUSIC-PA") of Iordache et al [9], conceptually based on the multiple signal classification algorithm [29,30], successfully avoids this potential drawback by operating on the entire image at once. The algorithm does so by representing the original image as a small set of eigenvectors and subsequently calculating the distance from each library entry to this simplified representation.…”

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.…”