{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T19:02:33Z","timestamp":1771700553168,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,4]],"date-time":"2021-10-04T00:00:00Z","timestamp":1633305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science and Technology Research Program for Universities in Shandong Province","award":["J16LI58"],"award-info":[{"award-number":["J16LI58"]}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2018LA003"],"award-info":[{"award-number":["ZR2018LA003"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province","award":["DRN19020"],"award-info":[{"award-number":["DRN19020"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11801060"],"award-info":[{"award-number":["11801060"]}],"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":["11501082"],"award-info":[{"award-number":["11501082"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Research and Development Project of Dezhou City in China","award":["no"],"award-info":[{"award-number":["no"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>X-ray computed tomography (CT) is widely used in medical applications, where many efforts have been made for decades to eliminate artifacts caused by incomplete projection. In this paper, we propose a new CT image reconstruction model based on nonlocal low-rank regularity and data-driven tight frame (NLR-DDTF). Unlike the Spatial-Radon domain data-driven tight frame regularization, the proposed NLR-DDTF model uses an asymmetric treatment for image reconstruction and Radon domain inpainting, which combines the nonlocal low-rank approximation method for spatial domain CT image reconstruction and data-driven tight frame-based regularization for Radon domain image inpainting. An alternative direction minimization algorithm is designed to solve the proposed model. Several numerical experiments and comparisons are provided to illustrate the superior performance of the NLR-DDTF method.<\/jats:p>","DOI":"10.3390\/sym13101873","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T01:59:47Z","timestamp":1633917587000},"page":"1873","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["CT Image Reconstruction via Nonlocal Low-Rank Regularization and Data-Driven Tight Frame"],"prefix":"10.3390","volume":"13","author":[{"given":"Yanfeng","family":"Shen","sequence":"first","affiliation":[{"name":"School of Mathematics and Big Data, Dezhou University, Dezhou 253023, China"},{"name":"Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuli","family":"Sun","sequence":"additional","affiliation":[{"name":"Financial Department of Dezhou University, Dezhou 253023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fengsheng","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Big Data, Dezhou University, Dezhou 253023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanqin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Big Data, Dezhou University, Dezhou 253023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiuling","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Mathematics and Big Data, Dezhou University, Dezhou 253023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoshuang","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Big Data, Dezhou University, Dezhou 253023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/s10915-012-9579-6","article-title":"X-ray ct image reconstruction via wavelet frame based regularization and radon domain inpainting","volume":"54","author":"Dong","year":"2013","journal-title":"J. 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