Solving the inverse problem of compressive sensing in the context of single measurement vector (SMV) problem with an unknown block-sparsity structure is considered. For this purpose, we propose a sparse Bayesian learning (SBL) algorithm simplified via the approximate message passing (AMP) framework. In order to encourage the block-sparsity structure, we incorporate the concept of total variation, called Sigma-Delta, as a measure of block-sparsity on the support set of the solution. The AMP framework reduces the computational load of the proposed SBL algorithm and as a result makes it faster compared to the message passing framework. Furthermore, in terms of the mean-squared error between the true and the reconstructed solution, the algorithm demonstrates an encouraging improvement compared to the other algorithms.
Shekaramiz, Mohammad, Moon, Todd K., and Gunther, Jacob H. "Details on AMP-B-SBL: An Algorithm for Recovery of Clustered Sparse Signals Using Approximate Message Passing [1-3]." 2019, pp. 1-25.