Unmixing sparse hyperspectral mixtures

Finding an accurate sparse approximation of a spectral vector described by a linear model, when there is available a library of possible constituent signals (called endmembers or atoms), is a hard combinatorial problem which, as in other areas, has been increasingly addressed. This paper studies the efficiency of the sparse regression techniques in the spectral unmixing problem by conducting a comparison between four different approaches: Moore-Penrose Pseudoinverse, Orthogonal Matching Pursuit (OMP), Iterative Spectral Mixture Analysis (ISMA) and l₂ - l₁ sparse regression techniques, which are of widespread use in compressed sensing. We conclude that the l₂-l₁ sparse regression techniques, implemented here by Iterative Shrinkage/Thresholding (TwIST) algorithm, yield the state-of-the-art in the hyperspectral unmixing area.