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

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.