{"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/truncated-nuclear-norm-regularization-for-low","title":"Truncated nuclear norm regularization for low-rank tensor completion","arxiv_id":"1901.01997","date":"2019-01-07","proceeding":null,"authors":["Shengke Xue","Wenyuan Qiu","Fan Liu","Xinyu Jin"],"abstract":"Recently, low-rank tensor completion has become increasingly attractive in\nrecovering incomplete visual data. Considering a color image or video as a\nthree-dimensional (3D) tensor, existing studies have put forward several\ndefinitions of tensor nuclear norm. However, they are limited and may not\naccurately approximate the real rank of a tensor, and they do not explicitly\nuse the low-rank property in optimization. It is proved that the recently\nproposed truncated nuclear norm (TNN) can replace the traditional nuclear norm,\nas an improved approximation to the rank of a matrix. In this paper, we propose\na new method called the tensor truncated nuclear norm (T-TNN), which suggests a\nnew definition of tensor nuclear norm. The truncated nuclear norm is\ngeneralized from the matrix case to the tensor case. With the help of the low\nrankness of TNN, our approach improves the efficacy of tensor completion. We\nadopt the definition of the previously proposed tensor singular value\ndecomposition, the alternating direction method of multipliers, and the\naccelerated proximal gradient line search method in our algorithm. Substantial\nexperiments on real-world videos and images illustrate that the performance of\nour approach is better than those of previous methods.","url_abs":"http://arxiv.org/abs/1901.01997v1","url_pdf":"http://arxiv.org/pdf/1901.01997v1.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":"truncated-nuclear-norm-regularization-for-low","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}