{"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/a-novel-nonconvex-approach-to-recover-the-low","title":"Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm","arxiv_id":"1712.05870","date":"2017-12-15","proceeding":null,"authors":["Tai-Xiang Jiang","Ting-Zhu Huang","Xi-Le Zhao","Liang-Jian Deng"],"abstract":"In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the tensor tubal multi-rank. We build two PSTNN-based minimization models for two typical tensor recovery problems, i.e., the tensor completion and the tensor principal component analysis. We give two algorithms based on the alternating direction method of multipliers (ADMM) to solve proposed PSTNN-based tensor recovery models. Experimental results on the synthetic data and real-world data reveal the superior of the proposed PSTNN.","url_abs":"https://arxiv.org/abs/1712.05870v3","url_pdf":"https://arxiv.org/pdf/1712.05870v3.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":"a-novel-nonconvex-approach-to-recover-the-low","repo_url":"https://github.com/TaiXiangJiang/PSTNN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-novel-nonconvex-approach-to-recover-the-low","repo_url":"https://github.com/uestctensorgroup/PSTNN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-novel-nonconvex-approach-to-recover-the-low","repo_url":"https://github.com/zhaoxile/Multi-dimensional-imaging-data-recovery-via-minimizing-the-partial-sum-of-tubal-nuclear-norm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-novel-nonconvex-approach-to-recover-the-low","repo_url":"https://github.com/zhaoxile/PSTNN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}