{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/low-rank-tensor-completion-by-truncated","title":"Low-Rank Tensor Completion by Truncated Nuclear Norm Regularization","arxiv_id":"1712.00704","date":"2017-12-03","proceeding":null,"authors":["Shengke Xue","Wenyuan Qiu","Fan Liu","Xinyu Jin"],"abstract":"Currently, low-rank tensor completion has gained cumulative attention in\nrecovering incomplete visual data whose partial elements are missing. By taking\na color image or video as a three-dimensional (3D) tensor, previous studies\nhave suggested several definitions of tensor nuclear norm. However, they have\nlimitations and may not properly approximate the real rank of a tensor.\nBesides, they do not explicitly use the low-rank property in optimization. It\nis proved that the recently proposed truncated nuclear norm (TNN) can replace\nthe traditional nuclear norm, as a better estimation to the rank of a matrix.\nThus, this paper presents a new method called the tensor truncated nuclear norm\n(T-TNN), which proposes a new definition of tensor nuclear norm and extends the\ntruncated nuclear norm from the matrix case to the tensor case. Beneficial from\nthe low rankness of TNN, our approach improves the efficacy of tensor\ncompletion. We exploit the previously proposed tensor singular value\ndecomposition and the alternating direction method of multipliers in\noptimization. Extensive experiments on real-world videos and images demonstrate\nthat the performance of our approach is superior to those of existing methods.","url_abs":"http://arxiv.org/abs/1712.00704v5","url_pdf":"http://arxiv.org/pdf/1712.00704v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"low-rank-tensor-completion-by-truncated","repo_url":"https://github.com/xueshengke/Tensor-TNNR","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}