A Novel Hierarchical Bayesian Approach for Sparse

Abstract—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 abun-dances, 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 it-erative method is derived, and its connection with Gibbs sampling and variational Bayesian inference is highlighted. Experimental re-sults 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. Index Terms—Compressive sensing, constrained optimization, constrained sparse regression, hierarchical Bayesian analysis, hy-perspectral imagery, sparse semisupervised unmixing. I