{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T07:16:14Z","timestamp":1779261374884,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T00:00:00Z","timestamp":1681689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671213"],"award-info":[{"award-number":["11671213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701411"],"award-info":[{"award-number":["11701411"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671213"],"award-info":[{"award-number":["11671213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701411"],"award-info":[{"award-number":["11701411"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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 P-norm minimization approach, the GOMP is easier to implement, and the assumption of \u03b3-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.<\/jats:p>","DOI":"10.3390\/axioms12040389","type":"journal-article","created":{"date-parts":[[2023,4,18]],"date-time":"2023-04-18T01:36:45Z","timestamp":1681781805000},"page":"389","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Efficiency of Orthogonal Matching Pursuit for Group Sparse Recovery"],"prefix":"10.3390","volume":"12","author":[{"given":"Chunfang","family":"Shao","sequence":"first","affiliation":[{"name":"College of Science, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiujie","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Sciences, Tianjin Chengjian University, Tianjin 300384, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peixin","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5585-6215","authenticated-orcid":false,"given":"Shuo","family":"Xing","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Foucart, S., and Rauhut, H. 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