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 [France]

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.

Keywords: group sparsity; block coordinate relaxation; sensor selection; beamforming

Domains: Signal and Image processing

Thierry Chonavel, Abdeldjalil Aissa El Bey, Zahran Hajji. Iterative Descent Group Hard Thresholding Algorithms for Block Sparsity. Signal Processing, 2023, 212, pp.109182. ⟨10.1016/j.sigpro.2023.109182⟩. ⟨hal-04156466v2⟩