{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T23:08:06Z","timestamp":1778972886137,"version":"3.51.4"},"publisher-location":"Cham","reference-count":31,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031976377","type":"print"},{"value":"9783031976384","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,6,28]],"date-time":"2025-06-28T00:00:00Z","timestamp":1751068800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,6,28]],"date-time":"2025-06-28T00:00:00Z","timestamp":1751068800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-031-97638-4_27","type":"book-chapter","created":{"date-parts":[[2025,7,6]],"date-time":"2025-07-06T09:02:24Z","timestamp":1751792544000},"page":"430-446","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Assessment of\u00a0Alternating Projection Methods for\u00a0Matrix Completion with\u00a0Application to\u00a0Sparse Image Reconstruction"],"prefix":"10.1007","author":[{"given":"Mattia","family":"Silei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefania","family":"Bellavia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simone","family":"Rebegoldi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,28]]},"reference":[{"key":"27_CR1","doi-asserted-by":"crossref","unstructured":"Agarwal, A., Amjad, M.J., Shah, D., Shen, D.: Model agnostic time series analysis via matrix estimation. In: Proceedings of the ACM on Measurement and Analysis of Computing Systems, vol.\u00a02, pp. 1\u201339. ACM New York, NY, USA (2018)","DOI":"10.1145\/3287319"},{"issue":"2","key":"27_CR2","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1287\/moor.1100.0449","volume":"35","author":"H Attouch","year":"2010","unstructured":"Attouch, H., Bolte, J., Redont, P., Soubeyran, A.: Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-\u0141ojasiewicz inequality. Math. Oper. Res. 35(2), 438\u2013457 (2010)","journal-title":"Math. Oper. Res."},{"key":"27_CR3","doi-asserted-by":"publisher","unstructured":"Attouch, H., Redont, P., Soubeyran, A.: A new class of alternating proximal minimization algorithms with costs-to-move. SIAM J. Optim. 18(3), 1061\u20131081 (2007). https:\/\/doi.org\/10.1137\/060657248, https:\/\/doi.org\/10.1137\/060657248","DOI":"10.1137\/060657248"},{"key":"27_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/conm\/204\/02620","volume":"204","author":"HH Bauschke","year":"1997","unstructured":"Bauschke, H.H., Borwein, J.M., Lewis, A.S.: The method of cyclic projections for closed convex sets in Hilbert space. Contemp. Math. 204, 1\u201338 (1997)","journal-title":"Contemp. Math."},{"key":"27_CR5","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/BF01027691","volume":"1","author":"HH Bauschke","year":"1993","unstructured":"Bauschke, H.H., Borwein, J.M.: On the convergence of von Neumann\u2019s alternating projection algorithm for two sets. Set-Valued Anal. 1, 185\u2013212 (1993)","journal-title":"Set-Valued Anal."},{"issue":"3","key":"27_CR6","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1137\/S0036144593251710","volume":"38","author":"HH Bauschke","year":"1996","unstructured":"Bauschke, H.H., Borwein, J.M.: On projection algorithms for solving convex feasibility problems. SIAM Rev. 38(3), 367\u2013426 (1996)","journal-title":"SIAM Rev."},{"key":"27_CR7","doi-asserted-by":"publisher","unstructured":"Behling, R., Bello-Cruz, Y., Santos, L.R.: Infeasibility and error bound imply finite convergence of alternating projections. SIAM J. Optim. 31(4), 2863\u20132892 (2021). https:\/\/doi.org\/10.1137\/20M1358669, https:\/\/doi.org\/10.1137\/20M1358669","DOI":"10.1137\/20M1358669"},{"issue":"2","key":"27_CR8","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1007\/s10915-021-01654-1","volume":"89","author":"S Bellavia","year":"2021","unstructured":"Bellavia, S., Gondzio, J., Porcelli, M.: A relaxed interior point method for low-rank semidefinite programming problems with applications to matrix completion. J. Sci. Comput. 89(2), 46 (2021)","journal-title":"J. Sci. Comput."},{"key":"27_CR9","unstructured":"Bellavia, S., Rebegoldi, S., Silei, M.: An Inexact Alternating Projection Method with Application to Matrix Completion. Optimization Online (2025)"},{"issue":"4","key":"27_CR10","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1137\/050644641","volume":"17","author":"J Bolte","year":"2007","unstructured":"Bolte, J., Daniilidis, A., Lewis, A.: The \u0141ojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. SIAM J. Optim. 17(4), 1205\u20131223 (2007)","journal-title":"SIAM J. Optim."},{"issue":"6","key":"27_CR11","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1145\/2184319.2184343","volume":"55","author":"E Candes","year":"2012","unstructured":"Candes, E., Recht, B.: Exact matrix completion via convex optimization. Commun. ACM 55(6), 111\u2013119 (2012)","journal-title":"Commun. ACM"},{"key":"27_CR12","doi-asserted-by":"publisher","first-page":"2007","DOI":"10.1007\/s11063-019-10163-0","volume":"51","author":"O Elharrouss","year":"2020","unstructured":"Elharrouss, O., Almaadeed, N., Al-Maadeed, S., Akbari, Y.: Image inpainting: a review. Neural Process. Lett. 51, 2007\u20132028 (2020)","journal-title":"Neural Process. Lett."},{"key":"27_CR13","doi-asserted-by":"publisher","unstructured":"Escalante, R., Raydan, M.: Alternating Projection Methods. Society for Industrial and Applied Mathematics, Philadelphia, PA (2011).https:\/\/doi.org\/10.1137\/9781611971941, https:\/\/epubs.siam.org\/doi\/abs\/10.1137\/9781611971941","DOI":"10.1137\/9781611971941"},{"key":"27_CR14","doi-asserted-by":"crossref","unstructured":"Golub, G.H., Van\u00a0Loan, C.F.: Matrix Computations. JHU Press (2013)","DOI":"10.56021\/9781421407944"},{"key":"27_CR15","doi-asserted-by":"crossref","unstructured":"Guerreiro, R., Aguiar, P.: Estimation of rank deficient matrices from partial observations: two-step iterative algorithms. In: International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, pp. 450\u2013466. Springer (2003)","DOI":"10.1007\/978-3-540-45063-4_29"},{"issue":"5","key":"27_CR16","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1109\/LSP.2017.2685518","volume":"24","author":"X Jiang","year":"2017","unstructured":"Jiang, X., Zhong, Z., Liu, X., So, H.C.: Robust matrix completion via alternating projection. IEEE Signal Process. Lett. 24(5), 579\u2013583 (2017)","journal-title":"IEEE Signal Process. Lett."},{"issue":"4","key":"27_CR17","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1007\/s10208-008-9036-y","volume":"9","author":"A Lewis","year":"2009","unstructured":"Lewis, A., Luke, D.R., Malick, J.: Local linear convergence of alternating and averaged nonconvex projections. Found. Comput. Math. 9(4), 485\u2013513 (2009)","journal-title":"Found. Comput. Math."},{"issue":"2","key":"27_CR18","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1109\/TSMCB.2011.2168953","volume":"42","author":"K Li","year":"2012","unstructured":"Li, K., Dai, Q., Xu, W., Yang, J., Jiang, J.: Three-dimensional motion estimation via matrix completion. IEEE Trans. Syst. Man Cybern. 42(2), 539\u2013551 (2012)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"27_CR19","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s10851-012-0406-3","volume":"47","author":"DR Luke","year":"2013","unstructured":"Luke, D.R.: Prox-regularity of rank constraint sets and implications for algorithms. J. Math. Imag. Vis. 47, 231\u2013238 (2013)","journal-title":"J. Math. Imag. Vis."},{"issue":"1","key":"27_CR20","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/s10107-009-0306-5","volume":"128","author":"S Ma","year":"2011","unstructured":"Ma, S., Goldfarb, D., Chen, L.: Fixed point and Bregman iterative methods for matrix rank minimization. Math. Program. 128(1), 321\u2013353 (2011)","journal-title":"Math. Program."},{"key":"27_CR21","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.jvcir.2016.01.004","volume":"36","author":"M Nejati","year":"2016","unstructured":"Nejati, M., Samavi, S., Derksen, H., Najarian, K.: Denoising by low-rank and sparse representations. J. Vis. Commun. Image Represent. 36, 28\u201339 (2016)","journal-title":"J. Vis. Commun. Image Represent."},{"key":"27_CR22","volume-title":"Functional operators, Annals of Mathematics Studies","author":"J von Neumann","year":"2010","unstructured":"von Neumann, J.: Functional operators, Annals of Mathematics Studies, vol. 22. Princeton University Press, Princeton, NJ (2010)"},{"key":"27_CR23","doi-asserted-by":"publisher","first-page":"94215","DOI":"10.1109\/ACCESS.2019.2928130","volume":"7","author":"LT Nguyen","year":"2019","unstructured":"Nguyen, L.T., Kim, J., Shim, B.: Low-rank matrix completion: a contemporary survey. IEEE Access 7, 94215\u201394237 (2019)","journal-title":"IEEE Access"},{"key":"27_CR24","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/s10208-015-9253-0","volume":"16","author":"D Noll","year":"2016","unstructured":"Noll, D., Rondepierre, A.: On local convergence of the method of alternating projections. Found. Comput. Math. 16, 425\u2013455 (2016)","journal-title":"Found. Comput. Math."},{"issue":"3","key":"27_CR25","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1190\/1.3552706","volume":"76","author":"V Oropeza","year":"2011","unstructured":"Oropeza, V., Sacchi, M.: Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis. Geophysics 76(3), 25\u201332 (2011)","journal-title":"Geophysics"},{"issue":"4","key":"27_CR26","doi-asserted-by":"publisher","first-page":"308","DOI":"10.26599\/BDMA.2018.9020008","volume":"1","author":"A Ramlatchan","year":"2018","unstructured":"Ramlatchan, A., Yang, M., Liu, Q., Li, M., Wang, J., Li, Y.: A survey of matrix completion methods for recommendation systems. Big Data Mining Anal. 1(4), 308\u2013323 (2018)","journal-title":"Big Data Mining Anal."},{"key":"27_CR27","doi-asserted-by":"crossref","unstructured":"Rennie, J., Srebro, N.: Fast maximum margin matrix factorization for collaborative prediction. In: Proceedings of the International Conference of Machine Learning, pp. 713\u2013719 (2005)","DOI":"10.1145\/1102351.1102441"},{"key":"27_CR28","doi-asserted-by":"publisher","unstructured":"Silei, M., Bellavia, S., Superchi, F., Bianchini, A.: Recovering corrupted data in wind farm measurements: a matrix completion approach. Energies 16(4) (2023). https:\/\/doi.org\/10.3390\/en16041674, https:\/\/www.mdpi.com\/1996-1073\/16\/4\/1674","DOI":"10.3390\/en16041674"},{"issue":"1","key":"27_CR29","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1137\/1038003","volume":"38","author":"L Vandenberghe","year":"1996","unstructured":"Vandenberghe, L., Boyd, S.: Semidefinite Programming. SIAM Rev. 38(1), 49\u201395 (1996)","journal-title":"SIAM Rev."},{"issue":"2","key":"27_CR30","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s10915-021-01550-8","volume":"88","author":"H Wang","year":"2021","unstructured":"Wang, H., Cai, J., Wang, T., Wei, K.: Fast Cadzow\u2019s algorithm and a gradient variant. J. Sci. Comput. 88(2), 41 (2021)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"27_CR31","first-page":"3180612","volume":"2022","author":"X Xu","year":"2022","unstructured":"Xu, X., Geng, S.: Blind image inpainting with mixture noise using $$\\ell _0$$ and total regularization. Comput. Math. Meth. Med. 2022(1), 3180612 (2022)","journal-title":"Comput. Math. Meth. Med."}],"container-title":["Lecture Notes in Computer Science","Computational Science and Its Applications \u2013 ICCSA 2025 Workshops"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-97638-4_27","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T23:04:27Z","timestamp":1778972667000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-97638-4_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,28]]},"ISBN":["9783031976377","9783031976384"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-97638-4_27","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,28]]},"assertion":[{"value":"28 June 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that\u00a0are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"ICCSA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Computational Science and Its Applications","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Istanbul","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"T\u00fcrkiye","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30 June 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 July 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iccsa2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/iccsa.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}