Hyperspectral Image Recovery Using Nonconvex Sparsity and Low-Rank Regularizations

Hyperspectral image (HSI) restoration is an important preprocessing step in HSI data analysis to improve the image quality for subsequent applications of HSI. In this article, we introduce a spatial-spectral patch-based nonconvex sparsity and low-rank regularization method for HSI restoration. In contrast to traditional approaches based on convex penalties or nonconvex spectral penalty alone, we consider the sparsity of HSI in the spatial-spectral domain and combine the nonconvex low-rank penalty and the nonconvex 3-D total variation (TV)-like sparsity regularization to fully exploit the correlations in both spatial-spectral dimensions of the HSI data set. In addition, we propose a fast iterative variable splitting-based algorithm to effectively solve the corresponding optimization problem. Numerical experiments on both simulated and real HSI data sets demonstrate that the proposed nonconvex low-rank and TV (NonLRTV) method significantly improves the recovered image quality compared with the state-of-the-art algorithms.