Hyperspectral Sparse Unmixing via Nonconvex Shrinkage Penalties

Hyperspectral sparse unmixing aims at finding the optimal subset of spectral signatures in the given spectral library and estimating their proportions in each pixel. Recently, simultaneously sparse and low-rank representations (SSLRRs) have been widely used in the hyperspectral sparse unmixing task. This article developed a new unified framework to approximate the SSLRR-based unmixing model. The heart of the proposed framework is to design the new nonconvex penalties for efficient minimization by the means of two families of thresholding mappings, including the firm thresholding mapping and generalized shrinkage mapping. Both mappings can be regarded as generalizations of both soft thresholding and hard thresholding. Unlike previous approaches with explicit penalties, the proposed framework does not require explicit forms of penalties but only relevant thresholding mappings. Furthermore, an alternating direction method of multipliers (ADMM) was designed to solve the resulting optimization problem. Experiments conducted on the synthetic data and real data demonstrate the superiority of the proposed framework in improving the unmixing performance with respect to state-of-the-art methods.