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Since sparse unmixing has emerged as a promising approach to hyperspectralunmixing, some spatial-contextual information in the hyperspectral images hasbeen exploited to improve the performance of the unmixing recently. The totalvariation (TV) has been widely used to promote the spatial homogeneity as wellas the smoothness between adjacent pixels. However, the computation task forhyperspectral sparse unmixing with a TV regularization term is heavy. Besides,the convergence of the primal alternating direction method of multipliers(ADMM) for the hyperspectral sparse unmixing with a TV regularization term hasnot been explained in details. In this paper, we design an efficient andconvergent dual symmetric Gauss-Seidel ADMM (sGS-ADMM) for hyperspectral sparseunmixing with a TV regularization term. We also present the global convergenceand local linear convergence rate analysis for this algorithm. As demonstratedin numerical experiments, our algorithm can obviously improve the efficiency ofthe unmixing compared with the state-of-the-art algorithm. More importantly, wecan obtain images with higher quality.

A Dual Symmetric Gauss-Seidel Alternating Direction Method of Multipliers for Hyperspectral Sparse Unmixing