Sparse Estimation with Generalized Beta Mixture and the Horseshoe Prior
This work addresses signal recovery in compressive sensing, an incremental advancement with potential applications in domains like imaging and communications.
The paper tackles the problem of sparse signal recovery in compressive sensing by proposing a Bayesian framework using Generalized Beta Mixture and Horseshoe priors, resulting in algorithms that outperform state-of-the-art methods in reconstruction accuracy, convergence rate, and sparsity, with the largest improvements for high-amplitude signals.
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.