A Two-Level Simultaneous Orthogonal Matching Pursuit Algorithm for Simultaneous Sparse Approximation Problems

A Two-Level Simultaneous Orthogonal Matching Pursuit Algorithm for Simultaneous Sparse Approximation Problems

Year:    2023

Author:    Nian Shao, Rui Zhang, Jie Sun, Wenbin Chen

CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 4 : pp. 758–775

Abstract

In this paper, we propose a two-level simultaneous orthogonal matching pursuit (TLSOMP) algorithm for simultaneous sparse approximation (SSA) problems. Most existing algorithms for SSA problems are directly generalized from the ones for the sparse approximation (SA) problems, for example, the simultaneous orthogonal matching pursuit (SOMP) method is generalized from the orthogonal matching pursuit (OMP) method. Our newly proposed algorithm is designed from another viewpoint. We first analyze the noiseless case and propose a selection algorithm. Motivated by the analysis and presuming noise as a perturbation, we extend the selection algorithm into a TLSOMP algorithm. This novel algorithm mainly uses the information from the subspace spanned by the multiple signals, which is not available in SA problems. Numerical experiments show the superiority of our TLSOMP algorithm over other traditional SSA solvers.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/csiam-am.SO-2022-0050

CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 4 : pp. 758–775

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Simultaneous sparse approximation two-level simultaneous orthogonal matching pursuit subspace approximation.

Author Details

Nian Shao

Rui Zhang

Jie Sun

Wenbin Chen