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However, the low\u2010rank prior may not be enough to recover the original tensor from the observed incomplete tensor. In this paper, we propose a tensor completion method to recover color images and gray videos by exploiting both the low\u2010rank and sparse prior of the observed tensor. Specifically, the tensor completion task can be formulated as a low\u2010rank minimization problem with a sparse regularizer. The low\u2010rank property is depicted by the tensor truncated nuclear norm based on tensor singular value decomposition which is a better approximation of tensor tubal rank than tensor nuclear norm. While the sparse regularizer is imposed by a \u2113<\/jats:italic>1<\/jats:sub>\u2010norm in a discrete cosine transformation domain, which can better employ the local sparse property of the incomplete data. To solve the optimization problem, we employ an alternating direction method of multipliers in which we only need to solve several subproblems which have closed\u2010form solutions. Substantial experiments on real\u2010world images and videos show that the proposed method has better performances than the existing state\u2010of\u2010the\u2010art methods.<\/jats:p>","DOI":"10.1002\/nla.2387","type":"journal-article","created":{"date-parts":[[2021,5,10]],"date-time":"2021-05-10T10:24:32Z","timestamp":1620642272000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Low\u2010rank tensor completion with sparse regularization in a transformed domain"],"prefix":"10.1002","volume":"28","author":[{"given":"Ping\u2010Ping","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences University of Electronic Science and Technology of China Chengdu P.R. 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