Compressed sensing of different size block-sparse signals: Efficient recovery

Abstract

This paper considers compressed sensing of different size block-sparse signals, i.e. signals with nonzero elements occurring in blocks with different lengths. A new sufficient condition for mixed l2/l1-optimization algorithm is derived to successfully recover k-sparse signals. We show that if the signal possesses k-block sparse structure, then via mixed l2/l1-optimization algorithm, a better reconstruction results can be achieved in comparison with the conventional l1-optimization algorithm and fixed-size mixed l2/l1-optimization algorithm. The significance of the results presented in this paper lies in the fact that making explicit use of different block-sparsity can yield better reconstruction properties than treating the signal as being sparse in the conventional sense, thereby ignoring the structure in the signal.Index Terms-Compressed sensing, block-sparsity, mixed l2/l1-optimization algorithm.