Sparse Estimation with Generalized Beta Mixture and the Horseshoe Prior

TL;DR

This paper introduces novel Bayesian priors based on the Generalized Beta Mixture and Horseshoe distributions for sparse signal recovery, resulting in faster algorithms that outperform existing methods especially for high-amplitude sparse signals.

Contribution

It develops explicit EM-update algorithms for Bayesian compressive sensing using GBM and Horseshoe priors, enhancing recovery performance and convergence speed.

Findings

Algorithms outperform state-of-the-art methods in accuracy

Faster convergence rates demonstrated

Significant improvements for high-amplitude sparse signals

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.