Endmember Distinguished Low-Rank and Sparse Representation for Hyperspectral Unmixing

Hyperspectral unmixing has become a valuable research area in recent years. As significant characteristics of hyperspectral images (HSIs), low-rankness and sparsity have been widely studied to improve the accuracy of abundance estimation for spectral unmixing. However, most of the existing models perform the low-rank and sparse constraints on the entire abundance matrix at the same time, ignoring that low-rankness is often only caused by a few active endmembers. In this paper, we propose a simple but effective method to separate endmembers that contribute more to low-rank property from the given spectral dictionary, and then exploit the weighted nuclear norm on their corresponding abundance maps to enhance the low-rankness. In addition, to make full use of sparsity, both spectral and spatial weighted factors are considered in the ℓ
1
-norm to constrain abundances of all endmembers. The proposed algorithm is based on the alternating direction method of multipliers (ADMM) framework. Simulated and real-data experiments demonstrate the effectiveness of the resulting unmixing algorithm.