  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 endmembers 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.
