Sparse Hyperspectral Unmixing

Given a set of mixed spectral vectors, spectral mixture analysis (or spectral unmixing) aims at estimating the number of reference materials, also called endmembers, their spectral signatures, and their fractional abundances. A semi-supervised approach to deal with the linear spectral unmixing problem consists in assuming that the observed spectral vectors are linear combinations of a small number of spectral signatures known in advance. Unmixing then amounts to find a small number of materials in the spectral library that best represent the observed data. Finding a small number of signatures in a large library is a combinatorial problem which calls for efficient sparse regression techniques. In this study, we compare four unmixing algorithms with the ultimate goal of analyzing their potential in solving sparse hyperspectral unmixing problems. The algorithms compared are: 1) Moore-Penrose pseudoinverse; 2) Orthogonal Matching Pursuit algorithm (Y. Pati, et al. ,1993); 3) ISMA – Iterative Spectral Mixture Analysis (D. Rogge, et al., 2006); 4) TwIST (Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration) algorithm (J. Bioucas-Dias and M. Figueiredo, 2007). After conducting a quantitative and comparative analysis of the above-mentioned algorithms, we conclude that the 1 2 l l − sparse regression techniques and the respective algorithms, of which TwIST is an example, yield state-of-the-art performance in hyperspectral sparse unmixing; this conclusion is in line with the success that these optimization methods have achieved in the area of compressed sensing. * Corresponding author