Bayesian Hypothesis Testing for Block Sparse Signal Recovery
This work addresses signal recovery in compressed sensing for applications like communications or imaging, but it appears incremental as it builds on existing Bayesian and MMSE methods without claiming broad breakthroughs.
The paper tackles the problem of reconstructing block sparse signals with unknown block structures by proposing a Block Bayesian Hypothesis Testing Algorithm (Block-BHTA), which combines Bayesian hypothesis testing for support detection and linear MMSE for amplitude estimation, and demonstrates its effectiveness through numerical experiments.
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.