Hyperspectral image unmixing via bilinear generalized approximate message passing

In hyperspectral unmixing, the objective is to decompose an electromagnetic spectral dataset measured over M spectral bands and T pixels, into N constituent material spectra (or “endmembers”) with corresponding spatial abundances. In this paper, we propose a novel approach to hyperspectral unmixing (i.e., joint estimation of endmembers and abundances) based on loopy belief propagation. In particular, we employ the bilinear generalized approximate message passing algorithm (BiG-AMP), a recently proposed belief-propagation-based approach to matrix factorization, in a “turbo” framework that enables the exploitation of spectral coherence in the endmembers, as well as spatial coherence in the abundances. In conjunction, we propose an expectationmaximization (EM) technique that can be used to automatically tune the prior statistics assumed by turbo BiG-AMP. Numerical experiments on synthetic and real-world data confirm the state-of-the-art performance of our approach.