Graph-Based Blind Hyperspectral Unmixing via Nonnegative Matrix Factorization

Hyperspectral unmixing (HU) is a crucial step in the hyperspectral image (HSI) analysis. It aims at decomposing the observed spectrum at each pixel into a collection of constituent endmembers, weighted by their abundances. In a close spatial neighborhood, due to spatial autocorrelation, the abundances of an endmember tend to be similar to each other. Therefore, the spectra at the neighboring pixels are also very much alike. Recently, many studies have focused on graph-regularized nonnegative matrix factorization (NMF) approaches to address the blind HU problem. This is mainly because graph structures allow spatial-spectral relations to be effectively embedded in the NMF framework. This article takes one step further by defining each abundance map as a signal on a suitable graph, which enables the HU problem to be analyzed for the first time from a graph signal processing perspective. This article introduces a novel Laplacian regularizer based on the l
₁
-norm, where graph spectral analysis is utilized to show that the regularizer has natural piecewise smooth (PWS) signal promotion and noise rejection capabilities. A graph-based blind HU algorithm is developed by incorporating this regularizer and an l
_1/2
-abundance sparsity constraint into the NMF problem. Since the featured regularizer exploits the PWS property of abundance maps, the proposed method is effective in HU. The experiments conducted on synthetic and real HSIs demonstrate that it has superior performance compared with several popular HU algorithms.