Sufficient condition for exact support recovery of sparse signals through greedy block coordinate descent

In the underdetermined model Y ^ = A X + N , where X is a K-group sparse matrix (i.e. it has no more than K non-zero rows), the matrix A may be also perturbed. Theoretically, a more relaxed condition means that fewer measurements are required to ensure sparse recovery. In this study, a relaxed sufficient condition is proposed for greedy block coordinate descent (GBCD) under total perturbations based on the restricted isometry property in order to guarantee that the support of X is recovered. We also show that GBCD fails in a more general case when 1 / ( K + 1 ) ≤ δ K + 1 < 1 .