Block-sparse compressed sensing: non-convex model and iterative re-weighted algorithm

摘要

Compressed sensing is a new sampling technique which can exactly reconstruct sparse signal from a few measurements. In this article, we consider the block-sparse compressed sensing with special structure assumption about the signal. A novel non-convex model is proposed to reconstruct the block-sparse signals. In addition, the conditions of the proposed model for recovering the block-sparse noise or noise-free signals are presented. The experimental results demonstrate that the proposed non-convex method surpasses the convex method (the mixed l_2/l_1-norm optimization) and some algorithms without considering the block-sparse structure (the l_1- and l_p-norm optimization).