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.