{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T08:13:03Z","timestamp":1759133583301,"version":"3.41.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,6,16]],"date-time":"2015-06-16T00:00:00Z","timestamp":1434412800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2016,1]]},"DOI":"10.1007\/s10589-015-9769-x","type":"journal-article","created":{"date-parts":[[2015,6,15]],"date-time":"2015-06-15T03:49:56Z","timestamp":1434340196000},"page":"169-202","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["An iterative algorithm for third-order tensor multi-rank minimization"],"prefix":"10.1007","volume":"63","author":[{"given":"Lei","family":"Yang","sequence":"first","affiliation":[]},{"given":"Zheng-Hai","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Shenglong","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Jiye","family":"Han","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,6,16]]},"reference":[{"key":"9769_CR1","doi-asserted-by":"crossref","DOI":"10.1002\/0471787779","volume-title":"Nonlinear Programming","author":"MS Bazaraa","year":"2006","unstructured":"Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming, 3rd edn. Wiley, New York (2006)","edition":"3"},{"issue":"1","key":"9769_CR2","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1177\/109434209200600103","volume":"6","author":"MW Berry","year":"1992","unstructured":"Berry, M.W.: Large-scale sparse singular value decompositions. Int. J. Supercomput. Appl. 6(1), 13\u201349 (1992)","journal-title":"Int. J. Supercomput. Appl."},{"key":"9769_CR3","doi-asserted-by":"crossref","DOI":"10.1145\/344779.344972","volume-title":"Image Inpainting","author":"M Bertalm\u00edo","year":"2000","unstructured":"Bertalm\u00edo, M., Sapiro, G., Caselles, V., Ballester, C.: Image Inpainting. Proceedings of SIGGRAPH, New Orleans (2000)"},{"issue":"7","key":"9769_CR4","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.1016\/j.laa.2010.05.025","volume":"433","author":"K Braman","year":"2010","unstructured":"Braman, K.: Third-order tensors as linear operators on a space of matrices. Linear Algebra Appl. 433(7), 1241\u20131253 (2010)","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"9769_CR5","doi-asserted-by":"crossref","first-page":"1956","DOI":"10.1137\/080738970","volume":"20","author":"JF Cai","year":"2010","unstructured":"Cai, J.F., Cand\u00e8s, E.J., Shen, Z.W.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956\u20131982 (2010)","journal-title":"SIAM J. Optim."},{"issue":"6","key":"9769_CR6","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1007\/s10208-009-9045-5","volume":"9","author":"EJ Cand\u00e8s","year":"2009","unstructured":"Cand\u00e8s, E.J., Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. 9(6), 717\u2013772 (2009)","journal-title":"Found. Comput. Math."},{"key":"9769_CR7","first-page":"1","volume-title":"Mathematics in Signal Processing V","author":"P Comon","year":"2001","unstructured":"Comon, P., et al.: Tensor decompositions: state of the art and applications. In: McWhirter, J., Proudler, I. (eds.) Mathematics in Signal Processing V, pp. 1\u201324. Oxford University Press, Oxford (2001)"},{"issue":"1","key":"9769_CR8","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1137\/S0097539704442696","volume":"36","author":"P Drineas","year":"2006","unstructured":"Drineas, P., Kannan, R., Mahoney, M.W.: Fast monte carlo algorithms for matrices II: computing low-rank approximations to a matrix. SIAM J. Comput. 36(1), 158\u2013183 (2006)","journal-title":"SIAM J. Comput."},{"key":"9769_CR9","doi-asserted-by":"crossref","unstructured":"Fazel, M., Hindi, H., Boyd, S.: A rank minimization heuristic with application to minimum order system approximation. Proceedings of the American Control Conference. (Arlington, VA, June 2001), 6, 4734\u20134739 (2001)","DOI":"10.1109\/ACC.2001.945730"},{"key":"9769_CR10","unstructured":"Fazel, M.: Matrix rank minimization with applications. PhD thesis, Stanford University (2002)"},{"key":"9769_CR11","doi-asserted-by":"crossref","unstructured":"Gandy, S., Recht, B., Yamada, I.: Tensor completion and low- $$n$$ n -rank tensor recovery via convex optimization. Inv.UD Probl. 27, 025010 (19pp) (2011)","DOI":"10.1088\/0266-5611\/27\/2\/025010"},{"key":"9769_CR12","volume-title":"Matrix Computations","author":"GH Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996)","edition":"3"},{"issue":"3","key":"9769_CR13","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1137\/070698920","volume":"19","author":"ET Hale","year":"2008","unstructured":"Hale, E.T., Yin, W.T., Zhang, Y.: A fixed-point continuation method for $$l_1$$ l 1 -regularized minimization with applications to compressed sensing. SIAM J. Optim. 19(3), 1107\u20131130 (2008)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"9769_CR14","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1137\/110842570","volume":"6","author":"N Hao","year":"2013","unstructured":"Hao, N., Kilmer, M.E., Braman, K., Hoover, R.C.: Facial recognition using tensor\u2013tensor decomposition. SIAM J. Imaging Sci. 6(1), 437\u2013463 (2013)","journal-title":"SIAM J. Imaging Sci."},{"issue":"4","key":"9769_CR15","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/0196-6774(90)90014-6","volume":"11","author":"J H\u00e5stad","year":"1990","unstructured":"H\u00e5stad, J.: Tensor rank is NP-complete. J. Algorithms 11(4), 644\u2013654 (1990)","journal-title":"J. Algorithms"},{"key":"9769_CR16","unstructured":"Kilmer, M.E., Martin, C.D., Perrone, L.: A third-order generalization of the matrix SVD as a product of third-order tensors. Technical Report TR-2008-4, Department of Computer Science, Tufts University, Medford, MA (2008)"},{"issue":"1","key":"9769_CR17","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1137\/110837711","volume":"34","author":"ME Kilmer","year":"2013","unstructured":"Kilmer, M.E., 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."},{"issue":"3","key":"9769_CR18","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/j.laa.2010.09.020","volume":"435","author":"ME Kilmer","year":"2011","unstructured":"Kilmer, M.E., Martin, C.D.: Factorization strategies for third-order tensors. Linear Algebra Appl. 435(3), 641\u2013658 (2011)","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"9769_CR19","doi-asserted-by":"crossref","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":"9769_CR20","first-page":"442","volume":"1","author":"N Komodakis","year":"2006","unstructured":"Komodakis, N.: Image completion using global optimization. CVPR 1, 442\u2013452 (2006)","journal-title":"CVPR"},{"issue":"9","key":"9769_CR21","doi-asserted-by":"crossref","first-page":"2262","DOI":"10.1109\/TIP.2007.903263","volume":"16","author":"T Korah","year":"2007","unstructured":"Korah, T., Rasmussen, C.: Spatiotemporal inpainting for recovering texture maps of occluded building facades. IEEE Trans. Image Process. 16(9), 2262\u20132271 (2007)","journal-title":"IEEE Trans. Image Process."},{"key":"9769_CR22","volume-title":"Three-Mode Principal Component Analysis: Theory and Applications","author":"P Kroonenberg","year":"1983","unstructured":"Kroonenberg, P.: Three-Mode Principal Component Analysis: Theory and Applications. DSWO Press, Leiden (1983)"},{"key":"9769_CR23","unstructured":"Larsen, R.M.: PROPACK-software for large and sparse svd calculations available at http:\/\/sun.stanford.edu\/srmunk\/PROPACK\/"},{"key":"9769_CR24","first-page":"1","volume-title":"Mathematics in Signal Processing IV","author":"LDe Lathauwer","year":"1998","unstructured":"Lathauwer, LDe, Moor, B.D.: From matrix to tensor: multilinear algebra and signal processing. In: McWhirter, J., Proudler, E.I. (eds.) Mathematics in Signal Processing IV, pp. 1\u201315. Clarendon Press, Oxford (1998)"},{"key":"9769_CR25","doi-asserted-by":"crossref","unstructured":"Liu, J., Musialski, P., Wonka, P., Ye, J.P.: Tensor completion for estimating missing values in visual data. IEEE Int. Conf. Computer Vision (ICCV), Kyoto, Japan, pp. 2114\u20132121 (2009)","DOI":"10.1109\/ICCV.2009.5459463"},{"issue":"1\u20132","key":"9769_CR26","first-page":"321","volume":"128","author":"SQ Ma","year":"2011","unstructured":"Ma, S.Q., Goldfarb, D., Chen, L.F.: Fixed point and Bregman iterative methods for matrix rank minimization. Math. Program. 128(1\u20132), 321\u2013353 (2011)","journal-title":"Math. Program."},{"issue":"3","key":"9769_CR27","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1137\/070697835","volume":"52","author":"B Recht","year":"2010","unstructured":"Recht, B., Fazel, M., Parrilo, P.A.: Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev. 52(3), 471\u2013501 (2010)","journal-title":"SIAM Rev."},{"key":"9769_CR28","first-page":"3413","volume":"12","author":"B Recht","year":"2011","unstructured":"Recht, B.: A simpler approach to matrix completion. J. Mach. Learn. Res. 12, 3413\u20133430 (2011)","journal-title":"J. Mach. Learn. Res."},{"key":"9769_CR29","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"issue":"4","key":"9769_CR30","doi-asserted-by":"crossref","first-page":"1678","DOI":"10.1109\/TIP.2014.2305840","volume":"23","author":"O Semerci","year":"2014","unstructured":"Semerci, O., 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":"9769_CR31","unstructured":"Signoretto, M., Lathauwer L.De., Suykens J.A.K.: Nuclear norms for tensors and their use for convex multilinear estimation, Preprint, submitted to Linear Algebra Appl., September (2010)"},{"key":"9769_CR32","doi-asserted-by":"crossref","DOI":"10.1002\/0470012110","volume-title":"Multi-way Analysis: Applications in the Chemical Sciences","author":"A Smilde","year":"2004","unstructured":"Smilde, A., Bro, R., Geladi, P.: Multi-way Analysis: Applications in the Chemical Sciences. Wiley, New York (2004)"},{"key":"9769_CR33","first-page":"615","volume":"6","author":"KC Toh","year":"2010","unstructured":"Toh, K.C., Yun, S.W.: An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems. Pac. J. Optim. 6, 615\u2013640 (2010)","journal-title":"Pac. J. Optim."},{"key":"9769_CR34","unstructured":"Tomioka, R., Hayashi, K., Kashima, H.: Estimation of low-rank tensors via convex optimization (2011). arXiv:1010.0789v2"},{"issue":"3","key":"9769_CR35","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1023\/A:1017501703105","volume":"109","author":"P Tseng","year":"2001","unstructured":"Tseng, P.: Convergence of block coordinate descent method for nondifferentiable minimization. J. Optim. Theory Appl. 109(3), 475\u2013494 (2001)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"9769_CR36","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/0024-3795(92)90407-2","volume":"170","author":"GA Watson","year":"1992","unstructured":"Watson, G.A.: Characterization of the subdifferential of some matrix norms. Linear Algebra Appl. 170(1), 33\u201345 (1992)","journal-title":"Linear Algebra Appl."},{"key":"9769_CR37","doi-asserted-by":"crossref","unstructured":"Zhang, Z.M., Ely, G., Aeron, S., Hao, N., Kilmer, M.E.: Novel methods for multilinear data completion and de-noising based on tensor-SVD. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (2014)","DOI":"10.1109\/CVPR.2014.485"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-015-9769-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-015-9769-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-015-9769-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T16:41:04Z","timestamp":1748450464000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-015-9769-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,16]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["9769"],"URL":"https:\/\/doi.org\/10.1007\/s10589-015-9769-x","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"type":"print","value":"0926-6003"},{"type":"electronic","value":"1573-2894"}],"subject":[],"published":{"date-parts":[[2015,6,16]]}}}