Zhilin Zhang, Bhaskar D. Rao , Extension of SBL Algorithms for the Recovery of Block Sparse Signals with Intra-Block Correlation, submitted to IEEE Transaction on Signal Processing, January 2012
The associated codes can be downloaded here: https://sites.google.com/site/researchbyzhang/bsbl
Here is the abstract:
We examine the recovery of block sparse signals and extend the framework in two important directions; one by exploiting intra-block correlation and the other by generalizing the 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 partition. Another family, derived from an expanded bSBL framework, is based on a weaker assumption about the a priori information of the block structure, and can be used in the cases when block partition, block size, block sparsity are all unknown. Using these algorithms we show that exploiting intra-block correlation is very helpful to improve recovery performance. These algorithms also shed light on how to modify existing algorithms or design new ones to exploit such correlation for improved performance.
In this paper, we proposed three algorithms (BSBL-EM, BSBL-BO, BSBL-L1) for the block sparse model when block partition is known, and three algorithms (EBSBL-EM, EBSBL-BO, EBSBL-L1) for the model when block partition is unknown.
Here are some highlights:
 These algorithms have the best recovery performance among all the existing algorithms
I have spent more than one month to read published algorithms, downloaded their codes, performed experiments, and sending emails to authors to ask for optimal tuning of parameters, etc. I did't find any existing algorithms have better performance than mine. If you find one, please let me know.
Here is a comparison among all well-known algorithms when block partition is given (signal length was fixed while we changed the measurement number; see the paper for details) :
Here is a comparison among existing algorithms when block partition is unknown (signal length, measurement number, and the number of nonzero elements in the signal were fixed while we changed the nonzero block number; each block had random size and location. See the paper for details)
 These algorithms are the first algorithms that adaptively exploit intra-block correlation, i.e. the correlation among elements of a block.
 We revealed that intra-block correlation, if exploited, can significantly improve recovery performance and reduce the number of measurements.
Here is an experiment result showing our algorithms have better performance when intra-block correlation increases (see the paper for details)
 We also found that the intra-block correlation has little effects on the performance of existing algorithms. This is different to our finding on the MMV model, where we found temporal correlation has obvious negative effects on the performance of existing algorithms (for temporal correlation on the algorithm performance, see here).
Here is an experiment result showing the performance of Block-CoSaMP and Block-OMP is almost not affected by the intra-block correlation (see the paper for details).