Iterative Descent Group Hard Thresholding Algorithms for Block Sparsity

Thierry Chonavel (1, 2) , Abdeldjalil Aissa El Bey (1, 3) , Zahran Hajji (4)

1 IMT Atlantique - MEE - Département Mathematical and Electrical Engineering
2 Lab-STICC_MATRIX - Equipe Models and AlgoriThms for pRocessIng and eXtracting information
3 Lab-STICC_COSYDE - Equipe Communication System Design
4 NXP Semiconductors

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.

Keywords: group sparsity, block coordinate relaxation, l_2,0 regularization, sensor selection, beamforming.

Mots clés: group sparsity; block coordinate relaxation; l_2; 0 regularization; sensor selection; beamforming

Domaines: Sciences de l'ingénieur [physics]; Traitement du signal et de l'image [eess.SP]

Thierry Chonavel, Abdeldjalil Aissa El Bey, Zahran Hajji. Iterative Descent Group Hard Thresholding Algorithms for Block Sparsity. Signal Processing, 2023, 212 (November), pp.109182. ⟨10.1016/j.sigpro.2023.109182⟩. ⟨hal-04156466v1⟩