{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:35Z","timestamp":1760242235420,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,2,21]],"date-time":"2017-02-21T00:00:00Z","timestamp":1487635200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Compressive principal component pursuit (CPCP) recovers a target matrix that is a superposition of low-complexity structures from a small set of linear measurements. Pervious works mainly focus on the analysis of the existence and uniqueness. In this paper, we address its stability. We prove that the solution to the related convex programming of CPCP gives an estimate that is stable to small entry-wise noise. We also provide numerical simulation results to support our result. Numerical results show that the solution to the related convex program is stable to small entry-wise noise under board condition.<\/jats:p>","DOI":"10.3390\/a10010029","type":"journal-article","created":{"date-parts":[[2017,2,22]],"date-time":"2017-02-22T11:40:52Z","timestamp":1487763652000},"page":"29","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stable Analysis of Compressive Principal Component Pursuit"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1806-1560","authenticated-orcid":false,"given":"Qingshan","family":"You","sequence":"first","affiliation":[{"name":"School of Computer Science, Civil Aviation Flight University of China, Guanghan 618307, China"},{"name":"School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}]},{"given":"Qun","family":"Wan","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1007\/s10208-009-9045-5","article-title":"Exact matrix completion via convex optimzation","volume":"9","author":"Recht","year":"2009","journal-title":"Found. Comput. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1109\/JPROC.2009.2035722","article-title":"Matrix completion with noise","volume":"98","author":"Plan","year":"2010","journal-title":"Proc. IEEE"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1109\/TIT.2010.2044061","article-title":"The power of convex relaxation: Near-optimal matrix completion","volume":"56","author":"Tao","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_4","unstructured":"Ellenberg, J. (2010). Fill in the blanks: Using math to turn lo-res datasets into hi-res samples. Wired, Available online: https:\/\/www.wired.com\/2010\/02\/ff_algorithm\/all\/1."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Antonin Chambolle and Pierre-Louis Lions (1997). Image recovery via total variation minimization and related problems. Numer. Math., 76, 167\u2013188.","DOI":"10.1007\/s002110050258"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1190\/1.1440378","article-title":"Claerbout and Francis Muir. Robust modeling of erratic data","volume":"38","author":"Jon","year":"1973","journal-title":"Geophysics"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1109\/TCSVT.2008.918455","article-title":"Directional discrete cosine transforms: A new framework for image coding","volume":"18","author":"Zeng","year":"2011","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3736","DOI":"10.1109\/TIP.2006.881969","article-title":"Image denoising via sparse and redundant representations over learned dictionaries","volume":"15","author":"Elad","year":"2006","journal-title":"IEEE Trans. Image Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"9821","DOI":"10.1016\/j.eswa.2012.02.171","article-title":"Toward reducing failure risk in an integrated vehicle health maintenance system: A fuzzy multi-sensor data fusion Kalman filter approach for IVHMS","volume":"39","author":"Rodger","year":"2012","journal-title":"Expert Syst. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Cand\u00e8s, E.J., Li, X., Ma, Y., and Wright, J. (2011). Robust principal component analysis?. J. ACM.","DOI":"10.1145\/1970392.1970395"},{"key":"ref_11","unstructured":"Wright, J., Ganesh, A., Min, K., and Ma, Y. Compressive Principal Component Pursuit. Available online: http:\/\/yima.csl.illinois.edu\/psfile\/CPCP.pdf."},{"key":"ref_12","unstructured":"Recht, B., Fazel, M., and Parrilo, P. (arXiv, 2007). Guaranteed minimum rank solutions of matrix equations via nuclear norm minimization, arXiv."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhou, Z., Li, X., Wright, J., Cand\u00e8s, E.J., and Ma, Y. (arXiv, 2010). Stable Principal Component Pursuit, arXiv.","DOI":"10.1109\/ISIT.2010.5513535"},{"key":"ref_14","first-page":"167","article-title":"Sparse and low rank matrix decomposition via alternating direction method","volume":"9","author":"Yuan","year":"2009","journal-title":"Pac. J. Optim."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF02680549","article-title":"A variable-penalty alternating direction method for convex optimization","volume":"83","author":"Kontogiorgis","year":"1989","journal-title":"Math. Program."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/1\/29\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:28:48Z","timestamp":1760207328000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/10\/1\/29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,21]]},"references-count":15,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["a10010029"],"URL":"https:\/\/doi.org\/10.3390\/a10010029","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2017,2,21]]}}}