{"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/novel-methods-for-multilinear-data-completion","title":"Novel methods for multilinear data completion and de-noising based on tensor-SVD","arxiv_id":"1407.1785","date":"2014-07-07","proceeding":"CVPR 2014 6","authors":["Zemin Zhang","Gregory Ely","Shuchin Aeron","Ning Hao","Misha Kilmer"],"abstract":"In this paper we propose novel methods for completion (from limited samples)\nand de-noising of multilinear (tensor) data and as an application consider 3-D\nand 4- D (color) video data completion and de-noising. We exploit the recently\nproposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the\nnotion of multilinear rank and a related tensor nuclear norm was proposed in\n[11] to characterize informational and structural complexity of multilinear\ndata. We first show that videos with linear camera motion can be represented\nmore efficiently using t-SVD compared to the approaches based on vectorizing or\nflattening of the tensors. Since efficiency in representation implies\nefficiency in recovery, we outline a tensor nuclear norm penalized algorithm\nfor video completion from missing entries. Application of the proposed\nalgorithm for video recovery from missing entries is shown to yield a superior\nperformance over existing methods. We also consider the problem of tensor\nrobust Principal Component Analysis (PCA) for de-noising 3-D video data from\nsparse random corruptions. We show superior performance of our method compared\nto the matrix robust PCA adapted to this setting as proposed in [4].","url_abs":"http://arxiv.org/abs/1407.1785v2","url_pdf":"http://arxiv.org/pdf/1407.1785v2.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":"novel-methods-for-multilinear-data-completion","repo_url":"https://github.com/Nigoding/tensor-completion","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"novel-methods-for-multilinear-data-completion","repo_url":"https://github.com/jamiezeminzhang/Tensor_Completion_and_Tensor_RPCA","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1407.1785","atlas_url":"https://app.syntology.ai/?focus=1407.1785","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}