Bayesian Hypothesis Test using Nonparametric Belief Propagation for Noisy Sparse Recovery

TL;DR

This paper introduces BHT-BP, a Bayesian algorithm for noisy sparse recovery that combines support detection and estimation, demonstrating robustness to noise and improvements over existing methods.

Contribution

It presents a novel low-computational Bayesian framework using nonparametric belief propagation for noisy sparse recovery with LDPC-like matrices.

Findings

BHT-BP effectively detects support in noisy conditions.

The algorithm's performance varies with the minimum nonzero signal value.

BHT-BP outperforms CS-BP and is comparable to recent solvers.

Abstract

This paper proposes a low-computational Bayesian algorithm for noisy sparse recovery (NSR), called BHT-BP. In this framework, we consider an LDPC-like measurement matrices which has a tree-structured property, and additive white Gaussian noise. BHT-BP has a joint detection-and-estimation structure consisting of a sparse support detector and a nonzero estimator. The support detector is designed under the criterion of the minimum detection error probability using a nonparametric belief propagation (nBP) and composite binary hypothesis tests. The nonzeros are estimated in the sense of linear MMSE, where the support detection result is utilized. BHT-BP has its strength in noise robust support detection, effectively removing quantization errors caused by the uniform sampling-based nBP. Therefore, in the NSR problems, BHT-BP has advantages over CS-BP which is an existing nBP algorithm, being comparable to other recent CS solvers, in several aspects. In addition, we examine impact of the minimum nonzero value of sparse signals via BHT-BP, on the basis of the results of the recent literature. Our empirical result shows that variation of x_min is reflected to recovery performance in the form of SNR shift.