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In this paper the problem of semisupervised hyper spectral 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 nonnegativity 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. Experimental results on both synthetic and real hyperspectral data illustrate that the proposed method converges fast, favors sparsity in the abun dances' vector, and offers improved estimation accuracy compared to other related methods.