Iterative descent group hard thresholding algorithms for block sparsity

Abstract

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 ℓ2,1 mixed norm penalty terms is often used as a convex alternative to the ℓ2,0 penalty. Here, we propose an iterative block cyclic descent algorithm approach to address the case of an ℓ2,0 penalty. We prove its convergence and illustrate its potential benefit compared to ℓ2,1 or ℓ2,q (0<q≤1) penalization. We also propose a momentum approach for accelerated convergence and an application to sensor positioning for array processing.