Convex optimization problems are common in hyperspectral unmixing. Examplesinclude: the constrained least squares (CLS) and the fully constrained leastsquares (FCLS) problems, which are used to compute the fractional abundances inlinear mixtures of known spectra; the constrained basis pursuit (CBP) problem,which is used to find sparse (i.e., with a small number of non-zero terms)linear mixtures of spectra from large libraries; the constrained basis pursuitdenoising (CBPDN) problem, which is a generalization of BP that admits modelingerrors. In this paper, we introduce two new algorithms to efficiently solvethese optimization problems, based on the alternating direction method ofmultipliers, a method from the augmented Lagrangian family. The algorithms aretermed SUnSAL (sparse unmixing by variable splitting and augmented Lagrangian)and C-SUnSAL (constrained SUnSAL). C-SUnSAL solves the CBP and CBPDN problems,while SUnSAL solves CLS and FCLS, as well as a more general version thereof,called constrained sparse regression (CSR). C-SUnSAL and SUnSAL are shown tooutperform off-the-shelf methods in terms of speed and accuracy.
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