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In this paper the problem of semi-supervised hyperspectral unmixing is considered. More specifically, the unmixing process is formulated as a linear regression problem, where the abundance's physical constraints are taken into account. Based on this formulation, a novel hierarchical Bayesian model is proposed and suitable priors are selected for the model parameters such that, on the one hand, they ensure the non-negativity of the abundances, while on the other hand they favor sparse solutions for the abundances' vector. Performing Bayesian inference based on the proposed hierarchical Bayesian model, a new low-complexity iterative method is derived, and its connection with Gibbs sampling and variational Bayesian inference is highlighted.
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