{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T01:54:26Z","timestamp":1778032466450,"version":"3.51.4"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,11,1]],"date-time":"2020-11-01T00:00:00Z","timestamp":1604188800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,11,1]],"date-time":"2020-11-01T00:00:00Z","timestamp":1604188800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971159"],"award-info":[{"award-number":["11971159"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003803","name":"University of Hong Kong","doi-asserted-by":"publisher","award":["104005583"],"award-info":[{"award-number":["104005583"]}],"id":[{"id":"10.13039\/501100003803","id-type":"DOI","asserted-by":"publisher"}]},{"name":"HKRGC GRF","award":["12306616"],"award-info":[{"award-number":["12306616"]}]},{"name":"HKRGC GRF","award":["12200317"],"award-info":[{"award-number":["12200317"]}]},{"name":"HKRGC GRF","award":["12300218"],"award-info":[{"award-number":["12300218"]}]},{"name":"HKRGC GRF","award":["12300519"],"award-info":[{"award-number":["12300519"]}]},{"name":"HKRGC GRF","award":["17201020"],"award-info":[{"award-number":["17201020"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2020,11]]},"DOI":"10.1007\/s10915-020-01356-0","type":"journal-article","created":{"date-parts":[[2020,11,5]],"date-time":"2020-11-05T06:02:38Z","timestamp":1604556158000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Nonconvex Optimization for Robust Tensor Completion from Grossly Sparse Observations"],"prefix":"10.1007","volume":"85","author":[{"given":"Xueying","family":"Zhao","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9960-6138","authenticated-orcid":false,"given":"Minru","family":"Bai","sequence":"additional","affiliation":[]},{"given":"Michael K.","family":"Ng","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,11,5]]},"reference":[{"issue":"1\u20132","key":"1356_CR1","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s10107-011-0484-9","volume":"137","author":"H Attouch","year":"2013","unstructured":"Attouch, H., Bolte, J., Svaiter, B.F.: Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward\u2013backward splitting, and regularized Gauss\u2013Seidel methods. Math. Program. 137(1\u20132), 91\u2013129 (2013)","journal-title":"Math. Program."},{"issue":"3","key":"1356_CR2","doi-asserted-by":"publisher","first-page":"1637","DOI":"10.1137\/16M1084754","volume":"27","author":"MJ Ahn","year":"2017","unstructured":"Ahn, M.J., Pang, J.S., Xin, J.: Difference-of-convex learning: directional stationarity, optimality, and sparsity. SIAM J. Optim. 27(3), 1637\u20131665 (2017)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"1356_CR3","doi-asserted-by":"publisher","first-page":"1298","DOI":"10.1137\/15M1048008","volume":"9","author":"MR Bai","year":"2016","unstructured":"Bai, M.R., Zhang, X.J., Ni, G.Y., Cui, C.F.: An adaptive correction approach for tensor completion. SIAM J. Imaging Sci. 9(3), 1298\u20131323 (2016)","journal-title":"SIAM J. Imaging Sci."},{"key":"1356_CR4","doi-asserted-by":"publisher","first-page":"085004","DOI":"10.1088\/0266-5611\/32\/8\/085004","volume":"32","author":"MR Bai","year":"2016","unstructured":"Bai, M.R., Zhang, X.J., Shao, Q.Q.: Adaptive correction procedure for TVL1 image deblurring under impulse noise. Inverse Probl. 32, 085004 (2016)","journal-title":"Inverse Probl."},{"key":"1356_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03718-8","volume-title":"Real Algebraic Geometry. Ergeb. Math. Grenzgeb 36","author":"J Bochnak","year":"1998","unstructured":"Bochnak, J., Coste, M., Roy, M.F.: Real Algebraic Geometry. Ergeb. Math. Grenzgeb 36. Springer, Berlin (1998)"},{"issue":"1","key":"1356_CR6","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/s10107-013-0701-9","volume":"146","author":"J Bolte","year":"2014","unstructured":"Bolte, J., Sabach, S., Teboulle, M.: Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Program. 146(1), 459\u2013494 (2014)","journal-title":"Math. Program."},{"key":"1356_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1970392.1970395","volume":"58","author":"EJ Cand\u00e8s","year":"2011","unstructured":"Cand\u00e8s, E.J., Ma, Y., Wright, J., Li, X.: Robust principal component analysis? J. ACM 58, 1\u201337 (2011)","journal-title":"J. ACM"},{"key":"1356_CR8","doi-asserted-by":"publisher","first-page":"4589","DOI":"10.1109\/JSTARS.2017.2714338","volume":"10","author":"HY Fan","year":"2017","unstructured":"Fan, H.Y., Chen, Y.J., Guo, Y.L., Zhang, H.Y., Kuang, G.Y.: Hyperspectral image restoration using low-rank tensor recovery. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 10, 4589\u20134604 (2017)","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"issue":"456","key":"1356_CR9","doi-asserted-by":"publisher","first-page":"1348","DOI":"10.1198\/016214501753382273","volume":"96","author":"JQ Fan","year":"2001","unstructured":"Fan, J.Q., Li, R.Z.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc. 96(456), 1348\u20131360 (2001)","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"1356_CR10","doi-asserted-by":"publisher","first-page":"025010","DOI":"10.1088\/0266-5611\/27\/2\/025010","volume":"27","author":"S Gandy","year":"2011","unstructured":"Gandy, S., Recht, B., Yamada, I.: Tensor completion and low-n-rank tensor recovery via convex optimization. Inverse Probl. 27(2), 025010 (2011)","journal-title":"Inverse Probl."},{"issue":"1","key":"1356_CR11","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1137\/130905010","volume":"35","author":"D Goldfarb","year":"2014","unstructured":"Goldfarb, D., Qin, Z.W.: Robust low-rank tensor recovery: models and algorithms. SIAM J. Matrix Anal. Appl. 35(1), 225\u2013253 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"12","key":"1356_CR12","doi-asserted-by":"publisher","first-page":"125008","DOI":"10.1088\/1361-6420\/aa9383","volume":"33","author":"GY Gu","year":"2017","unstructured":"Gu, G.Y., Jiang, S.H., Yang, J.F.: A TVSCAD approach for image deblurring with impulse noise. Inverse Probl. 33(12), 125008 (2017)","journal-title":"Inverse Probl."},{"key":"1356_CR13","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1002\/sapm192761164","volume":"6","author":"FL Hitchcock","year":"1927","unstructured":"Hitchcock, F.L.: The expression of a tensor or a polyadic as a sum of products. J. Math. Phys. 6, 164\u2013189 (1927)","journal-title":"J. Math. Phys."},{"issue":"1","key":"1356_CR14","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1137\/140990309","volume":"26","author":"MY Hong","year":"2016","unstructured":"Hong, M.Y., Luo, Z.Q., Razaviyayn, M.: Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems. SIAM J. Optim. 26(1), 337\u2013364 (2016)","journal-title":"SIAM J. Optim."},{"key":"1356_CR15","doi-asserted-by":"crossref","unstructured":"Jiang, Q., Ng, M.: Robust low-tubal-rank tensor completion via convex optimization. In: Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, pp. 2649\u20132655 (2019)","DOI":"10.24963\/ijcai.2019\/368"},{"key":"1356_CR16","doi-asserted-by":"crossref","unstructured":"Karatzoglou, A., Amatriain, X., Baltrunas, L., Oliver, N.: Multiverse recommendation: n-dimensional tensor factorization for context-aware collaborative filtering. In: Proceedings of the fourth ACM Conference on Recommender Systems, pp. 79\u201386 (2010)","DOI":"10.1145\/1864708.1864727"},{"issue":"1","key":"1356_CR17","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1137\/110837711","volume":"34","author":"MW Kilmer","year":"2013","unstructured":"Kilmer, M.W., Braman, K., Hao, N., Hoover, R.C.: Third-order tensors as operators on matrices: a theoretical and computational framework with applications in imaging. SIAM J. Matrix Anal. Appl. 34(1), 148\u2013172 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1356_CR18","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1016\/j.laa.2010.09.020","volume":"435","author":"MW Kilmer","year":"2011","unstructured":"Kilmer, M.W., Martin, C.D.: Factorization strategies for third-order tensors. Linear Algebra Appl. 435, 641\u2013658 (2011)","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"1356_CR19","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455\u2013500 (2009)","journal-title":"SIAM Rev."},{"key":"1356_CR20","first-page":"1","volume-title":"Mathematics in Signal Processing IV","author":"LD Lathauwer","year":"1998","unstructured":"Lathauwer, L.D., Moor, B.D.: From matrix to tensor: multilinear algebra and signal processing. In: McWhirter, J., Proudler, I. (eds.) Mathematics in Signal Processing IV, pp. 1\u201315. Clarendon Press, Oxford (1998)"},{"issue":"1","key":"1356_CR21","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.cam.2017.09.029","volume":"331","author":"YF Li","year":"2018","unstructured":"Li, Y.F., Shang, K., Huang, Z.H.: Low Tucker rank tensor recovery via ADMM based on exact and inexact iteratively reweighted algorithms. J. Comput. Appl. Math. 331(1), 64\u201381 (2018)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"1356_CR22","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1109\/TPAMI.2012.39","volume":"35","author":"J Liu","year":"2013","unstructured":"Liu, J., Musialski, P., Wonka, P., Ye, J.: Tensor completion for estimating missing values invisual data. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 208\u2013220 (2013)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"4","key":"1356_CR23","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1109\/TPAMI.2019.2891760","volume":"42","author":"CY Lu","year":"2020","unstructured":"Lu, C.Y., Feng, J.S., Chen, Y.D., Liu, W., Lin, Z.C., Yan, S.: Tensor robust principal component analysis with a new tensor nuclear norm. IEEE Trans. Pattern Anal. Mach. Intell. 42(4), 925\u2013938 (2020)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"1","key":"1356_CR24","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1002\/widm.1","volume":"1","author":"M M\u00f8Rup","year":"2011","unstructured":"M\u00f8Rup, M.: Applications of tensor (multiway array) factorizations and decompositions in data mining. Wiley Interdiscip. Rev. Data Min. Knowl. Discov. 1(1), 24\u201340 (2011)","journal-title":"Wiley Interdiscip. Rev. Data Min. Knowl. Discov."},{"key":"1356_CR25","unstructured":"Mu, C., Huang, B., Wright, J., Goldfarb, D.: Square deal: lower bounds and improved relaxations for tensor recovery. In: Proceedings of the 31st International Conference on Machine Learning, vol. 32, pp. 73\u201381 (2014)"},{"key":"1356_CR26","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/s10107-015-0961-7","volume":"159","author":"WM Miao","year":"2016","unstructured":"Miao, W.M., Pan, S.H., Sun, D.F.: A rank-corrected procedure for matrix completion with fixed basis coefficients. Math. Program. 159, 289\u2013338 (2016)","journal-title":"Math. Program."},{"issue":"2","key":"1356_CR27","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1137\/S0097539792240406","volume":"24","author":"BK Natarajan","year":"1995","unstructured":"Natarajan, B.K.: Sparse approximate solutions to linear systems. SIAM J. Comput. 24(2), 227\u2013234 (1995)","journal-title":"SIAM J. Comput."},{"issue":"2","key":"1356_CR28","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1109\/TIP.2006.888343","volume":"16","author":"KA Patwardhan","year":"2007","unstructured":"Patwardhan, K.A., Sapiro, G., Bertalmio, M.: Video inpainting under constrained camera motion. IEEE Trans. Image Process. 16(2), 545\u2013553 (2007)","journal-title":"IEEE Trans. Image Process."},{"key":"1356_CR29","volume-title":"Variational Analysis","author":"RT Rockafellar","year":"1997","unstructured":"Rockafellar, R.T., Wets, R.J.: Variational Analysis. Springer, Berlin (1997)"},{"key":"1356_CR30","unstructured":"Romera-Paredes, B., Pontil, M.: A new convex relaxation for tensor completion. In: Proceedings of Advances in Neural Informance Processing Systems, vol. 26, pp. 2967\u20132975 (2013)"},{"key":"1356_CR31","unstructured":"Salakhutdinov, R., Srebro, N.: Collaborative filtering in a non-uniform world: learning with the weighted trace norm. In: Proceedings of Advances in Neural Informance Processing Systems, vol. 23,pp. 2056\u20132064 (2010)"},{"issue":"6","key":"1356_CR32","doi-asserted-by":"publisher","first-page":"2075","DOI":"10.1109\/23.819285","volume":"46","author":"AC Sauve","year":"1999","unstructured":"Sauve, A.C., Hero, A.O., Rogers, W.L., Wilderman, S.J., Clinthorne, N.H.: 3D image reconstruction for a compton spect camera model. IEEE Trans. Nucl. Sci. 46(6), 2075\u20132084 (1999)","journal-title":"IEEE Trans. Nucl. Sci."},{"issue":"4","key":"1356_CR33","doi-asserted-by":"publisher","first-page":"1678","DOI":"10.1109\/TIP.2014.2305840","volume":"23","author":"OS Semerci","year":"2014","unstructured":"Semerci, O.S., Hao, N., Kilmer, M.E., Miller, E.L.: Tensor-based formulation and nuclear norm regularization for multienergy computed tomography. IEEE Trans. Image Process. 23(4), 1678\u20131693 (2014)","journal-title":"IEEE Trans. Image Process."},{"key":"1356_CR34","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/s10994-013-5366-3","volume":"94","author":"M Signoretto","year":"2014","unstructured":"Signoretto, M., Dinh, Q.T., Lathauwer, L.D., Suykens, J.A.K.: Learning with tensors: a framework based on convex optimization and spectral regularization. Mach. Learn. 94, 303\u2013351 (2014)","journal-title":"Mach. Learn."},{"key":"1356_CR35","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1007\/s10444-017-9559-3","volume":"44","author":"T Sun","year":"2018","unstructured":"Sun, T., Yin, P.H., Cheng, L.Z., Jiang, H.: Alternating direction method of multipliers with difference of convex functions. Adv. Comput. Math. 44, 723\u2013744 (2018)","journal-title":"Adv. Comput. Math."},{"key":"1356_CR36","first-page":"289","volume":"22","author":"PD Tao","year":"1997","unstructured":"Tao, P.D., An, L.T.H.: Convex analysis approach to D.C. programming: theory, algorithms and applications. Acta Math. Vietnam. 22, 289\u2013355 (1997)","journal-title":"Acta Math. Vietnam."},{"key":"1356_CR37","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/0024-3795(84)90093-4","volume":"62","author":"PD Tao","year":"1984","unstructured":"Tao, P.D.: Convergence of a subgradient method for computing the bound norm of matrices. Linear Algebra Appl. 62, 163\u2013182 (1984)","journal-title":"Linear Algebra Appl."},{"key":"1356_CR38","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/S0304-0208(08)72402-2","volume":"129","author":"PD Tao","year":"1986","unstructured":"Tao, P.D., Bernoussi, S.E.: Algorithms for solving a class of nonconvex optimization problems. Methods of subgradients. North-Holl. Math. Stud. 129, 249\u2013271 (1986)","journal-title":"North-Holl. Math. Stud."},{"issue":"3","key":"1356_CR39","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/BF02289464","volume":"31","author":"LR Tucker","year":"1966","unstructured":"Tucker, L.R.: Some mathematical notes on three-mode factor analysis. Psychometrika 31(3), 279\u2013311 (1966)","journal-title":"Psychometrika"},{"key":"1356_CR40","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/s10915-018-0757-z","volume":"78","author":"Y Wang","year":"2019","unstructured":"Wang, Y., Yin, W.T., Zeng, J.S.: Global convergence of ADMM in nonconvex nonsmooth optimization. J. Sci. Comput. 78, 29\u201363 (2019)","journal-title":"J. Sci. Comput."},{"issue":"4","key":"1356_CR41","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TIP.2003.819861","volume":"13","author":"Z Wang","year":"2004","unstructured":"Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600\u2013612 (2004)","journal-title":"IEEE Trans. Image Process."},{"key":"1356_CR42","unstructured":"Wright, J., Peng, Y., Ma, Y., Ganesh, A., Rao, S.: Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization. In: Proceedings of Advances in Neural Informance Processing Systems, vol. 22, pp. 2080\u20132088 (2009)"},{"issue":"1","key":"1356_CR43","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1137\/15M1027528","volume":"10","author":"L Yang","year":"2017","unstructured":"Yang, L., Pong, T.K., Chen, X.J.: Alternating direction method of multipliers for a class of nonconvex and nonsmooth problems with applications to background\/foreground extraction. SIAM J. Imaging Sci. 10(1), 74\u2013110 (2017)","journal-title":"SIAM J. Imaging Sci."},{"issue":"9","key":"1356_CR44","doi-asserted-by":"publisher","first-page":"1933","DOI":"10.1109\/TNNLS.2015.2465178","volume":"27","author":"YN Yang","year":"2016","unstructured":"Yang, Y.N., Feng, Y.L., Suykens, J.A.K.: Robust low-rank tensor recovery with regularized redescending m-estimator. IEEE Trans. Neural Netw. Learn. Syst. 27(9), 1933\u20131946 (2016)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"2","key":"1356_CR45","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1214\/09-AOS729","volume":"38","author":"CH Zhang","year":"2010","unstructured":"Zhang, C.H.: Nearly unbiased variable selection under minimax concave penalty. Ann. Stat. 38(2), 894\u2013942 (2010)","journal-title":"Ann. Stat."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-020-01356-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-020-01356-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-020-01356-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,22]],"date-time":"2020-11-22T11:15:19Z","timestamp":1606043719000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-020-01356-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11]]},"references-count":45,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,11]]}},"alternative-id":["1356"],"URL":"https:\/\/doi.org\/10.1007\/s10915-020-01356-0","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11]]},"assertion":[{"value":"13 April 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 October 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 October 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 November 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"46"}}