Bayesian Hypothesis Test for Sparse Support Recovery using Belief Propagation

TL;DR

This paper presents BHT-BP, a Bayesian hypothesis testing algorithm using belief propagation for robust sparse support recovery from noisy measurements, outperforming traditional methods like OMP and Lasso in accuracy and efficiency.

Contribution

The paper introduces BHT-BP, a novel support recovery method that leverages belief propagation for robust, low-cost detection of sparse signals in noisy environments.

Findings

BHT-BP achieves higher support recovery accuracy than OMP and Lasso.

BHT-BP demonstrates robustness against measurement noise.

The algorithm has lower computational complexity compared to existing methods.

Abstract

In this paper, we introduce a new support recovery algorithm from noisy measurements called Bayesian hypothesis test via belief propagation (BHT-BP). BHT-BP focuses on sparse support recovery rather than sparse signal estimation. The key idea behind BHT-BP is to detect the support set of a sparse vector using hypothesis test where the posterior densities used in the test are obtained by aid of belief propagation (BP). Since BP provides precise posterior information using the noise statistic, BHT-BP can recover the support with robustness against the measurement noise. In addition, BHT-BP has low computational cost compared to the other algorithms by the use of BP. We show the support recovery performance of BHT-BP on the parameters (N; M; K; SNR) and compare the performance of BHT-BP to OMP and Lasso via numerical results.