Sparse Linear Spectral Unmixing of Hyperspectral images using Expectation-Propagation

This paper presents a novel Bayesian approach for hyperspectral image unmixing. The observed pixels are modeled by a linear combination of material signatures weighted by their corresponding abundances. A spike-and-slab abundance prior is adopted to promote sparse mixtures and an Ising prior model is used to capture spatial correlation of the mixture support across pixels. We approximate the posterior distribution of the abundances using the expectation-propagation (EP) method. We show that it can significantly reduce the computational complexity of the unmixing stage and meanwhile provide uncertainty measures, compared to expensive Monte Carlo strategies traditionally considered for uncertainty quantification. Moreover, many variational parameters within each EP factor can be updated in a parallel manner, which enables mapping of efficient algorithmic architectures based on graphics processing units (GPU). Under the same approximate Bayesian framework, we then extend the proposed algorithm to semi-supervised unmixing, whereby the abundances are viewed as latent variables and the expectation-maximization (EM) algorithm is used to refine the endmember matrix. Experimental results on synthetic data and real hyperspectral data illustrate the benefits of the proposed framework over state-of-art linear unmixing methods.