Hyperspectral Unmixing Via Nonconvex Sparse and Low-Rank Constraint

Abstract

In recent years, sparse unmixing has attracted significant attention, as it can effectively avoid the bottleneck problems associated with the absence of pure pixels and the estimation of the number of endmembers in hyperspectral scenes. The joint-sparsity model has outperformed the single sparse unmixing method. However, the joint-sparsity model might cause some aliasing artifacts for the pixels on the boundaries of different constituent endmembers. To address this shortcoming, researchers have developed many unmixing algorithms based on low-rank representation, which makes good use of the global structure of data. In addition, the high mutual coherence of spectral libraries strongly affects the applicability of sparse unmixing. In this study, adopting combined constraints imposing sparsity and low rankness, a novel algorithm called nonconvex joint-sparsity and low-rank unmixing with dictionary pruning is developed In particular, we impose sparsity on the abundance matrix using the $\ell _{2,p}$ mixed norm, and we also employ the weighted Schatten $p$ -norm instead of the convex nuclear norm as an approximation for the rank. The key parameter $p$ is set between 0.4 and 0.6, and a good quality sparse solution is generated. The effectiveness of the proposed algorithm is demonstrated on both simulated and real hyperspectral datasets.