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

Since sparse unmixing has emerged as a promising approach to hyperspectral unmixing, some spatial-contextual information in the hyperspectral images has been exploited to improve the performance of the unmixing recently. The total variation (TV) has been widely used to promote the spatial homogeneity as well as the smoothness between adjacent pixels. However, the computation task for hyperspectral sparse unmixing with a TV regularization term is heavy. Besides, the convergences of the traditional sparse unmixing algorithms which are special cases of the primal alternating direction method of multipliers (pADMM) have not been explained in details. In this paper, we design an efficient and convergent dual symmetric Gauss-Seidel ADMM (sGS-ADMM) for hyperspectral sparse unmixing with a TV regularization term. We also present the global convergence and local linear convergence rate analysis for the traditional sparse unmixing algorithm and our algorithm. As demonstrated in numerical experiments, our algorithm can obviously improve the efficiency of the unmixing compared with the state-of-the-art algorithm. More importantly, we can obtain images with higher quality.