Nonconvex-Sparsity and Nonlocal-Smoothness-Based Blind Hyperspectral Unmixing

Blind hyperspectral unmixing (HU), as a crucial technique for hyperspectral data exploitation, aims to decompose mixed pixels into a collection of constituent materials weighted by the corresponding fractional abundances. In recent years, nonnegative matrix factorization (NMF)-based methods have become more and more popular for this task and achieved promising performance. Among these methods, two types of properties upon the abundances, namely, the sparseness and the structural smoothness, have been explored and shown to be important for blind HU. However, all of the previous methods ignore another important insightful property possessed by a natural hyperspectral image (HSI), non-local smoothness, which means that similar patches in a larger region of an HSI are sharing the similar smoothness structure. Based on the previous attempts on other tasks, such a prior structure reflects intrinsic configurations underlying an HSI and is thus expected to largely improve the performance of the investigated HU problem. In this paper, we first consider such prior in HSI by encoding it as the non-local total variation (NLTV) regularizer. Furthermore, by fully exploring the intrinsic structure of HSI, we generalize NLTV to non-local HSI TV (NLHTV) to make the model more suitable for the blind HU task. By incorporating these two regularizers, together with a non-convex log-sum form regularizer characterizing the sparseness of abundance maps, to the NMF model, we propose novel blind HU models named NLTV/NLHTV and log-sum regularized NMF (NLTV-LSRNMF/NLHTV-LSRNMF), respectively. To solve the proposed models, an efficient algorithm is designed based on an alternative optimization strategy (AOS) and alternating direction method of multipliers (ADMM). Extensive experiments conducted on both simulated and real hyperspectral data sets substantiate the superiority of the proposed approach over other competing ones for blind HU task.