Linear spectral unmixing using collaborative sparse regression and correlated supports

This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the supports of the sparse abundance vectors are a priori spatially correlated across pixels. Secondly, we propose an advanced Markov chain Monte Carlo algorithm to estimate the posterior probabilities that materials are present or absent in each pixel, and, conditionally to the maximum marginal a posteriori configuration of this support, compute the MMSE estimates of the abundance vectors. A remarkable property of this algorithm is that it self-adjusts the values of the parameters of the Markov random field, thus relieving practitioners from setting regularisation parameters, namely by cross-validation. The proposed methodology is illustrated with real hyperspectral data.