Extension of SBL Algorithms for the Recovery of Block Sparse Signals With Intra-Block Correlation

TLDR

The study extends block sparse signal recovery by exploiting intra‑block correlation and generalizing block structure, proposing two families of block sparse Bayesian learning algorithms. One family, derived directly from BSBL, assumes known block structure, while the other, based on an expanded BSBL framework, operates with no prior block knowledge. Both families demonstrate that exploiting intra‑block correlation markedly improves recovery performance and provide guidance for adapting existing algorithms to leverage such correlation.

Abstract

We examine the recovery of block sparse signals and extend the framework in two important directions; one by exploiting signals' intra-block correlation and the other by generalizing signals' block structure. We propose two families of algorithms based on the framework of block sparse Bayesian learning (BSBL). One family, directly derived from the BSBL framework, requires knowledge of the block structure. Another family, derived from an expanded BSBL framework, is based on a weaker assumption on the block structure, and can be used when the block structure is completely unknown. Using these algorithms we show that exploiting intra-block correlation is very helpful in improving recovery performance. These algorithms also shed light on how to modify existing algorithms or design new ones to exploit such correlation and improve performance.