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Imaging Sci."],"published-print":{"date-parts":[[2024,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, a tensor completion method is proposed based on the Strassen\u2013Ottaviani flattening, which can reveal the underlying tensor rank intrinsically. The resulting tensor completion optimization problem is formulated by spectral functions (convex or nonconvex) as surrogates for the rank function. An exact recovery result for the nuclear norm surrogate is given. An efficient method is proposed for this problem, and adaptive parameters for the spectral functions are allowed during the iterations. The global convergence is established under mild assumptions on the spectral functions and the adaptive parameter updates. In particular, we show that the class of weighted nuclear norms (either with nonincreasing or nondecreasing weights), the [Formula: see text]-sparsity index, and a class of weighted nuclear norms with adaptive weights, which are all widely employed in the literature, all fulfill the assumptions, and thus the global convergence is valid without any assumption. Numerical experiments on color images show that the proposed methods are promising, and always return images with better quality than some state-of-the-art methods.<\/jats:p>","DOI":"10.1137\/23m158975x","type":"journal-article","created":{"date-parts":[[2024,12,2]],"date-time":"2024-12-02T14:00:51Z","timestamp":1733148051000},"page":"2242-2276","source":"Crossref","is-referenced-by-count":2,"title":["A Low-Rank Tensor Completion Method via Strassen\u2013Ottaviani Flattening"],"prefix":"10.1137","volume":"17","author":[{"given":"Tiantian","family":"He","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018 Zhejiang, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shenglong","family":"Hu","sequence":"additional","affiliation":[{"name":"Corresponding author. Department of Mathematics, College of Science, National University of Defense Technology, Changsha, 410072 Hunan, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2269-961X","authenticated-orcid":true,"given":"Zheng-Hai","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics and KL-AAGDM, Tianjin University, Tianjin, 300350 China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,12,2]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.chemolab.2010.08.004"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1974.223784"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/S0169-7439(98)00010-0"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-011-0484-9"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/15M1048008"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2017.2672439"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-002-0352-8"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-009-9045-5"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drq039"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/ast036"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971309"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-019-01044-8"},{"key":"ref13","unstructured":"M. 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