  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.
