Block-sparse recovery and rank minimization using a weighted lp−lq model

In this paper, we study a nonconvex, nonsmooth, and non-Lipschitz weighted l p − l q ( 0 < p ≤ 1 , 1 < q ≤ 2 ; 0 ≤ α ≤ 1 ) norm as a nonconvex metric to recover block-sparse signals and rank-minimization problems. Using block-RIP and matrix-RIP conditions, we obtain exact recovery results for block-sparse signals and rank minimization. We also obtain the theoretical bound for the block-sparse signals and rank minimization when measurements are degraded by noise.