Total Variation Regularized Reweighted Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing

Abstract

Blind hyperspectral unmixing (HU), which includes the estimation of endmembers and their corresponding fractional abundances, is an important task for hyperspectral analysis. Recently, nonnegative matrix factorization (NMF) and its extensions have been widely used in HU. Unfortunately, most of the NMF-based methods can easily lead to an unsuitable solution, due to the nonconvexity of the NMF model and the influence of noise. To overcome this limitation, we make the best use of the structure of the abundance maps, and propose a new blind HU method named total variation regularized reweighted sparse NMF (TV-RSNMF). First, the abundance matrix is assumed to be sparse, and a weighted sparse regularizer is incorporated into the NMF model. The weights of the weighted sparse regularizer are adaptively updated related to the abundance matrix. Second, the abundance map corresponding to a single fixed endmember should be piecewise smooth. Therefore, the TV regularizer is adopted to capture the piecewise smooth structure of each abundance map. In our multiplicative iterative solution to the proposed TV-RSNMF model, the TV regularizer can be regarded as an abundance map denoising procedure, which improves the robustness of TV-RSNMF to noise. A number of experiments were conducted in both simulated and real-data conditions to illustrate the advantage of the proposed TV-RSNMF method for blind HU.