{"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/incorporating-prior-information-in","title":"Incorporating Prior Information in Compressive Online Robust Principal Component Analysis","arxiv_id":"1701.06852","date":"2017-01-24","proceeding":null,"authors":["Huynh Van Luong","Nikos Deligiannis","Jurgen Seiler","Soren Forchhammer","Andre Kaup"],"abstract":"We consider an online version of the robust Principle Component Analysis\n(PCA), which arises naturally in time-varying source separations such as video\nforeground-background separation. This paper proposes a compressive online\nrobust PCA with prior information for recursively separating a sequences of\nframes into sparse and low-rank components from a small set of measurements. In\ncontrast to conventional batch-based PCA, which processes all the frames\ndirectly, the proposed method processes measurements taken from each frame.\nMoreover, this method can efficiently incorporate multiple prior information,\nnamely previous reconstructed frames, to improve the separation and thereafter,\nupdate the prior information for the next frame. We utilize multiple prior\ninformation by solving $n\\text{-}\\ell_{1}$ minimization for incorporating the\nprevious sparse components and using incremental singular value decomposition\n($\\mathrm{SVD}$) for exploiting the previous low-rank components. We also\nestablish theoretical bounds on the number of measurements required to\nguarantee successful separation under assumptions of static or slowly-changing\nlow-rank components. Using numerical experiments, we evaluate our bounds and\nthe performance of the proposed algorithm. In addition, we apply the proposed\nalgorithm to online video foreground and background separation from compressive\nmeasurements. Experimental results show that the proposed method outperforms\nthe existing methods.","url_abs":"http://arxiv.org/abs/1701.06852v2","url_pdf":"http://arxiv.org/pdf/1701.06852v2.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":"incorporating-prior-information-in","repo_url":"https://github.com/huynhlvd/corpca","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}