Bayesian Hypothesis Testing for Block Sparse Signal Recovery

TL;DR

This paper introduces a new Bayesian hypothesis testing algorithm for reconstructing block sparse signals with unknown structures, combining support detection and amplitude estimation, validated through numerical experiments.

Contribution

The paper proposes a novel Block Bayesian Hypothesis Testing Algorithm (Block-BHTA) for block sparse signal recovery with unknown block structures, integrating support detection and amplitude estimation.

Findings

Effective support detection and recovery demonstrated

Accurate amplitude estimation via linear MMSE

Validated through numerical experiments

Abstract

This letter presents a novel Block Bayesian Hypothesis Testing Algorithm (Block-BHTA) for reconstructing block sparse signals with unknown block structures. The Block-BHTA comprises the detection and recovery of the supports, and the estimation of the amplitudes of the block sparse signal. The support detection and recovery is performed using a Bayesian hypothesis testing. Then, based on the detected and reconstructed supports, the nonzero amplitudes are estimated by linear MMSE. The effectiveness of Block-BHTA is demonstrated by numerical experiments.