In this paper we consider the problem of recovering block-sparse structures in a linear regression context. Penalized mean squared criteria are generally considered in such contexts where l_2,1 mixed norm penalty terms is often used as a convex alternative to the l_2,0 penalty. Here, we propose an iterative block cyclic descent algorithm approach to address the case of an l_2,0 penalty. We prove its convergence and illustrate its potential benefit compared to l_2,1 or l_2,q (0 < q ≤ 1) penalization. We also propose a momentum approach for accelerated convergence and an application to sensor positioning for array processing.