Volume 4, Issue 4
A Two-Level Simultaneous Orthogonal Matching Pursuit Algorithm for Simultaneous Sparse Approximation Problems

Nian Shao, Rui Zhang, Jie Sun & Wenbin Chen

CSIAM Trans. Appl. Math., 4 (2023), pp. 758-775.

Published online: 2023-10

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  • 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.

  • AMS Subject Headings

65F20, 65F22, 65F55

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COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-4-758, author = {Shao , NianZhang , RuiSun , Jie and Chen , Wenbin}, title = {A Two-Level Simultaneous Orthogonal Matching Pursuit Algorithm for Simultaneous Sparse Approximation Problems}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2023}, volume = {4}, number = {4}, pages = {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.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2022-0050}, url = {http://global-sci.org/intro/article_detail/csiam-am/22077.html} }
TY - JOUR T1 - A Two-Level Simultaneous Orthogonal Matching Pursuit Algorithm for Simultaneous Sparse Approximation Problems AU - Shao , Nian AU - Zhang , Rui AU - Sun , Jie AU - Chen , Wenbin JO - CSIAM Transactions on Applied Mathematics VL - 4 SP - 758 EP - 775 PY - 2023 DA - 2023/10 SN - 4 DO - http://doi.org/10.4208/csiam-am.SO-2022-0050 UR - https://global-sci.org/intro/article_detail/csiam-am/22077.html KW - Simultaneous sparse approximation, two-level simultaneous orthogonal matching pursuit, subspace approximation. AB -

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.

Shao , NianZhang , RuiSun , Jie and Chen , Wenbin. (2023). A Two-Level Simultaneous Orthogonal Matching Pursuit Algorithm for Simultaneous Sparse Approximation Problems. CSIAM Transactions on Applied Mathematics. 4 (4). 758-775. doi:10.4208/csiam-am.SO-2022-0050
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