Bilateral Joint-Sparse Regression for Hyperspectral Unmixing

Sparse hyperspectral unmixing has been a hot topic in recent years. Joint sparsity assumes that each pixel in a small neighborhood of hyperspectral images (HSIs) is composed of the same endmembers, which results in a few nonzero rows in the abundance matrix. Recall that a plethora of unmixing algorithms transform a 3-D HSI into a 2-D matrix with vertical priority. The transformation makes matrix computation easier. It is, however, hard to maintain the horizontal spatial information in HSIs in many cases. To make further use of the spatial information of HSIs, in this article, we propose a
bilateral joint-sparse structure
for hyperspectral unmixing in an attempt to exploit the local joint sparsity of the abundance matrix in both the vertical and horizontal directions. In particular, we introduce a permutation matrix to realize the bilateral joint-sparse representation and there is no need to construct the matrix explicitly. Moreover, we propose to simultaneously impose the bilateral joint-sparse structure and low rankness on the abundance and develop a new algorithm named
bilateral joint-sparse and low-rank unmixing
. The proposed algorithm is based on the alternating direction method of multipliers framework and employs a reweighting strategy. The convergence analysis of the proposed algorithm is investigated. Simulated and real-data experiments show the effectiveness of the proposed algorithm.