Sparse Estimation with Generalized Beta Mixture and the Horseshoe Prior

Abstract: In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical model, making the corresponding inference problem amenable to Expectation Maximization (EM). We present an explicit, algebraic EM-update rule for the models, yielding two fast and experimentally validated algorithms for signal recovery. Experimental results show that our algorithms outperform state-of-the-art methods on a wide range of sparsity levels and amplitudes in terms of reconstruction accuracy, convergence rate and sparsity. The largest improvement can be observed for sparse signals with high amplitudes.