Efficiency of Orthogonal Matching Pursuit for Group Sparse Recovery
We propose the Group Orthogonal Matching Pursuit (GOMP) algorithm to recover group sparse signals from noisy measurements. Under the group restricted isometry property (GRIP), we prove the instance optimality of the GOMP algorithm for any decomposable approximation norm. Meanwhile, we show the robus...
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| Format: | Article |
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MDPI AG
2023-04-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/4/389 |
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| author | Chunfang Shao Xiujie Wei Peixin Ye Shuo Xing |
| author_facet | Chunfang Shao Xiujie Wei Peixin Ye Shuo Xing |
| author_sort | Chunfang Shao |
| collection | DOAJ |
| description | We propose the Group Orthogonal Matching Pursuit (GOMP) algorithm to recover group sparse signals from noisy measurements. Under the group restricted isometry property (GRIP), we prove the instance optimality of the GOMP algorithm for any decomposable approximation norm. Meanwhile, we show the robustness of the GOMP under the measurement error. Compared with the <i>P</i>-norm minimization approach, the GOMP is easier to implement, and the assumption of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-decomposability is not required. The simulation results show that the GOMP is very efficient for group sparse signal recovery and significantly outperforms Basis Pursuit in both scalability and solution quality. |
| first_indexed | 2024-03-11T05:14:46Z |
| format | Article |
| id | doaj.art-3a6414a7f9bf43ab954f8b56ffb641ce |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T05:14:46Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-3a6414a7f9bf43ab954f8b56ffb641ce2023-11-17T18:19:41ZengMDPI AGAxioms2075-16802023-04-0112438910.3390/axioms12040389Efficiency of Orthogonal Matching Pursuit for Group Sparse RecoveryChunfang Shao0Xiujie Wei1Peixin Ye2Shuo Xing3College of Science, North China University of Science and Technology, Tangshan 063210, ChinaSchool of Sciences, Tianjin Chengjian University, Tianjin 300384, ChinaSchool of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, ChinaSchool of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, ChinaWe propose the Group Orthogonal Matching Pursuit (GOMP) algorithm to recover group sparse signals from noisy measurements. Under the group restricted isometry property (GRIP), we prove the instance optimality of the GOMP algorithm for any decomposable approximation norm. Meanwhile, we show the robustness of the GOMP under the measurement error. Compared with the <i>P</i>-norm minimization approach, the GOMP is easier to implement, and the assumption of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-decomposability is not required. The simulation results show that the GOMP is very efficient for group sparse signal recovery and significantly outperforms Basis Pursuit in both scalability and solution quality.https://www.mdpi.com/2075-1680/12/4/389compressed sensinggroup orthogonal matching pursuitgroup sparsegroup restricted isometry propertyinstance optimalityrobustness |
| spellingShingle | Chunfang Shao Xiujie Wei Peixin Ye Shuo Xing Efficiency of Orthogonal Matching Pursuit for Group Sparse Recovery Axioms compressed sensing group orthogonal matching pursuit group sparse group restricted isometry property instance optimality robustness |
| title | Efficiency of Orthogonal Matching Pursuit for Group Sparse Recovery |
| title_full | Efficiency of Orthogonal Matching Pursuit for Group Sparse Recovery |
| title_fullStr | Efficiency of Orthogonal Matching Pursuit for Group Sparse Recovery |
| title_full_unstemmed | Efficiency of Orthogonal Matching Pursuit for Group Sparse Recovery |
| title_short | Efficiency of Orthogonal Matching Pursuit for Group Sparse Recovery |
| title_sort | efficiency of orthogonal matching pursuit for group sparse recovery |
| topic | compressed sensing group orthogonal matching pursuit group sparse group restricted isometry property instance optimality robustness |
| url | https://www.mdpi.com/2075-1680/12/4/389 |
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