{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T15:44:52Z","timestamp":1767109492424,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,18]],"date-time":"2019-12-18T00:00:00Z","timestamp":1576627200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of Korea(NRF)","award":["No. 2019R1F1A1060718","NRF-2018R1A6A3A01012976"],"award-info":[{"award-number":["No. 2019R1F1A1060718","NRF-2018R1A6A3A01012976"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we first propose a new TVL2 regularization model for image restoration, and then we propose two iterative methods, which are fixed-point and fixed-point-like methods, using CGLS (Conjugate Gradient Least Squares method) for solving the new proposed TVL2 problem. We also provide convergence analysis for the fixed-point method. Lastly, numerical experiments for several test problems are provided to evaluate the effectiveness of the proposed two iterative methods. Numerical results show that the new proposed TVL2 model is preferred over an existing TVL2 model and the proposed fixed-point-like method is well suited for the new TVL2 model.<\/jats:p>","DOI":"10.3390\/a13010001","type":"journal-article","created":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T09:50:33Z","timestamp":1576835433000},"page":"1","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Image Restoration Using a Fixed-Point Method for a TVL2 Regularization Problem"],"prefix":"10.3390","volume":"13","author":[{"given":"Kyoum Sun","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Mathematics, Chungbuk National University, Cheongju 28644, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6841-8137","authenticated-orcid":false,"given":"Jae Heon","family":"Yun","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Natural Sciences, Chungbuk National University, Cheongju 28644, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s002110050258","article-title":"Image recovery via total variation minimization and related problems","volume":"76","author":"Chambolle","year":"1997","journal-title":"Numer. 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