Bayesian linear unmixing of hyperspectral images corrupted by colored Gaussian noise with unknown covariance matrix

This paper addresses the problem of unmixing hyperspectral images contamined by additive colored noise. Each pixel of the image is modeled as a linear combination of pure materials (denoted as end-members) corrupted by an additive zero mean Gaussian noise sequence with unknown covariance matrix. Appropriate priors are defined ensuring positivity and additivity constraints on the mixture coefficients (denoted as abundances). These coefficients as well as the noise covariance matrix are then estimated from their joint posterior distribution. A Gibbs sampling strategy generates abundances and noise covariance matrices distributed according to the joint posterior. These samples are then averaged for minimum mean square error estimation.