{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:45:40Z","timestamp":1760060740729,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T00:00:00Z","timestamp":1758672000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12471290","120081","M202206"],"award-info":[{"award-number":["12471290","120081","M202206"]}]},{"name":"Suqian Sci&amp;Tech Program","award":["12471290","120081","M202206"],"award-info":[{"award-number":["12471290","120081","M202206"]}]},{"name":"Open Fund of the Key Laboratory of NSLSCS, Ministry of Education","award":["12471290","120081","M202206"],"award-info":[{"award-number":["12471290","120081","M202206"]}]},{"name":"Qing Lan Project","award":["12471290","120081","M202206"],"award-info":[{"award-number":["12471290","120081","M202206"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper addresses the NP-hard problem of solving the rank of a matrix in Robust Principal Component Analysis (RPCA) by proposing a nonconvex fractional regularization approximation. Compared to existing convex regularization (which often yields suboptimal solutions) and nonconvex regularization (which typically requires parameter selection), the proposed model effectively avoids parameter selection while preserving scale invariance. By introducing an auxiliary variable, we transform the problem into a nonconvex optimization problem with a separable structure. We use a more flexible Symmetric Alternating Direction Method of Multipliers (SADMM) to arrive at a solution and provide a rigorous convergence proof. In numerical experiments involving synthetic data, image recovery, and foreground\u2013background separation for surveillance video, the proposed fractional regularization model demonstrates high computational accuracy, and its performance is comparable to that of many state-of-the-art algorithms.<\/jats:p>","DOI":"10.3390\/sym17101590","type":"journal-article","created":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T08:19:45Z","timestamp":1758701985000},"page":"1590","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Nonconvex Fractional Regularization Model in Robust Principal Component Analysis via the Symmetric Alternating Direction Method of Multipliers"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1443-9666","authenticated-orcid":false,"given":"Zhili","family":"Ge","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Nanjing Normal University of Special Education, Nanjing 210038, China"}]},{"given":"Siyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Microelectronics and Data Science, Anhui University of Technology, Ma\u2019anshan 243032, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6649-1103","authenticated-orcid":false,"given":"Xin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Suqian University, Suqian 223800, China"},{"name":"Key Laboratory of Numerical Simulation for Large Scale Complex Systems, Ministry of Education, Nanjing 210023, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-4905-8313","authenticated-orcid":false,"given":"Yingying","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Southeast University, Nanjing 211189, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,24]]},"reference":[{"key":"ref_1","first-page":"11","article-title":"Robust principal component analysis?","volume":"58","author":"Li","year":"2011","journal-title":"J. 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