A perturbation analysis of block-sparse compressed sensing via mixed l(2)/l(1) minimization

摘要

In this paper, the recovery of block-sparse signals is considered by the completely perturbed mixed l(2)/l(1) minimization method and a sufficient condition is established to guarantee the robust recovery. The obtained result generalizes the existing result on complete perturbation to the block setting. Specially, we not only improve the condition related to block-restricted isometry property, but also better the error upper bound if the result degenerates to the general case. In addition, some numerical experiments are also carried out to demonstrate the block structure which is an important factor in the process of recovering block-sparse signals, and present outperformance of the mixed l(2)/l(1) minimization method comparing with the l(1) minimization method in the completely perturbed model.