Detection-Directed Sparse Estimation using Bayesian Hypothesis Test and Belief Propagation

TL;DR

This paper introduces a novel sparse recovery algorithm combining Bayesian hypothesis testing and belief propagation, which enhances noise robustness and reduces quantization effects, outperforming recent methods especially at high SNR.

Contribution

The paper presents a detection-directed sparse estimation algorithm using BHT and BP with sparse-binary matrices, offering improved noise robustness and quantization handling over existing approaches.

Findings

Algorithm approaches oracle estimator performance at high SNR.

Provides noise robustness beyond MAP-based methods.

Effectively removes quantization effects independently of memory size.

Abstract

In this paper, we propose a sparse recovery algorithm called detection-directed (DD) sparse estimation using Bayesian hypothesis test (BHT) and belief propagation (BP). In this framework, we consider the use of sparse-binary sensing matrices which has the tree-like property and the sampled-message approach for the implementation of BP. The key idea behind the proposed algorithm is that the recovery takes DD-estimation structure consisting of two parts: support detection and signal value estimation. BP and BHT perform the support detection, and an MMSE estimator finds the signal values using the detected support set. The proposed algorithm provides noise-robustness against measurement noise beyond the conventional MAP approach, as well as a solution to remove quantization effect by the sampled-message based BP independently of memory size for the message sampling. We explain how the proposed algorithm can have the aforementioned characteristics via exemplary discussion. In addition, our experiments validate such superiority of the proposed algorithm, compared to recent algorithms under noisy setup. Interestingly the experimental results show that performance of the proposed algorithm approaches that of the oracle estimator as SNR becomes higher.