Block-sparse signal recovery with synthesized multitask compressive sensing

The paper considers the problem of reconstructing blocks-sparse signals. A new algorithm, called synthesized multitask compressive sensing (SMCS), is proposed. In contrast to existing methods that rely on the availability of the sparsity structure information, the SMCS algorithm resorts to the multitask compressive sensing (MCS) technique for signal recovery. The SMCS algorithm synthesizes new compressive sensing (CS) tasks via circular-shifting operations and utilizes the minimum description length (MDL) principle to determine the proper set of the synthesized CS tasks for signal reconstruction. An outstanding advantage of SMCS is that it can achieve good signal reconstruction performance without using prior information on the block-sparsity structure. Simulations corroborate the theoretical developments.