{"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/robust-kronecker-decomposable-component","title":"Robust Kronecker-Decomposable Component Analysis for Low-Rank Modeling","arxiv_id":"1703.07886","date":"2017-03-22","proceeding":"ICCV 2017 10","authors":["Mehdi Bahri","Yannis Panagakis","Stefanos Zafeiriou"],"abstract":"Dictionary learning and component analysis are part of one of the most\nwell-studied and active research fields, at the intersection of signal and\nimage processing, computer vision, and statistical machine learning. In\ndictionary learning, the current methods of choice are arguably K-SVD and its\nvariants, which learn a dictionary (i.e., a decomposition) for sparse coding\nvia Singular Value Decomposition. In robust component analysis, leading methods\nderive from Principal Component Pursuit (PCP), which recovers a low-rank matrix\nfrom sparse corruptions of unknown magnitude and support. However, K-SVD is\nsensitive to the presence of noise and outliers in the training set.\nAdditionally, PCP does not provide a dictionary that respects the structure of\nthe data (e.g., images), and requires expensive SVD computations when solved by\nconvex relaxation. In this paper, we introduce a new robust decomposition of\nimages by combining ideas from sparse dictionary learning and PCP. We propose a\nnovel Kronecker-decomposable component analysis which is robust to gross\ncorruption, can be used for low-rank modeling, and leverages separability to\nsolve significantly smaller problems. We design an efficient learning algorithm\nby drawing links with a restricted form of tensor factorization. The\neffectiveness of the proposed approach is demonstrated on real-world\napplications, namely background subtraction and image denoising, by performing\na thorough comparison with the current state of the art.","url_abs":"http://arxiv.org/abs/1703.07886v2","url_pdf":"http://arxiv.org/pdf/1703.07886v2.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":"robust-kronecker-decomposable-component","repo_url":"https://github.com/mbahri/KDRSDL","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"dictionary-learning","task_name":"Dictionary Learning"},{"task_slug":"image-denoising","task_name":"Image Denoising"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}