Hyperspectral Unmixing Via Turbo Bilinear Approximate Message Passing

The goal of hyperspectral unmixing is to decompose an electromagnetic spectral dataset measured over M spectral bands and T pixels into N constituent material spectra (or “end-members”) with corresponding spatial abundances. In this paper, we propose a novel approach to hyperspectral unmixing based on loopy belief propagation (BP) that enables the exploitation of spectral coherence in the end-members and spatial coherence in the abundances. In particular, we partition the factor graph into spectral coherence, spatial coherence, and bilinear subgraphs, and pass messages between them using a “turbo” approach. To perform message passing within the bilinear subgraph, we employ the bilinear generalized approximate message passing algorithm (BiG-AMP), a recently proposed belief-propagation-based approach to matrix factorization. Furthermore, we propose an expectation-maximization (EM) strategy to tune the prior parameters and a model-order selection strategy to select the number of materials N. Numerical experiments conducted with both synthetic and real-world data show favorable unmixing performance relative to existing methods.