  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 convergence of the primal alternating direction method of multipliers
(ADMM) for the hyperspectral sparse unmixing with a TV regularization term has
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 this 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.
