Perturbation Analysis of Greedy Block Coordinate Descent Under RIP

Practically, in the underdetermined model Y = AX, where X is a K-group sparse matrix (i.e., it has no more than K nonzero rows), both Y and A could be totally perturbed. In this paper, based on restricted isometry property, for the greedy block coordinate descent algorithm, a sufficient condition of exact recovery is presented under the total perturbations, to guarantee that the support of the sparse matrix X is recovered exactly. It is pointed out that there exists some case satisfying our condition, but not the mutual coherence condition. We also discuss the upper bound of our sufficient condition.