{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:35:21Z","timestamp":1772296521436,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,7,6]],"date-time":"2017-07-06T00:00:00Z","timestamp":1499299200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2017,7,6]],"date-time":"2017-07-06T00:00:00Z","timestamp":1499299200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1522645"],"award-info":[{"award-number":["DMS-1522645"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,3]]},"DOI":"10.1007\/s10915-017-0492-x","type":"journal-article","created":{"date-parts":[[2017,7,6]],"date-time":"2017-07-06T08:08:39Z","timestamp":1499328519000},"page":"1241-1263","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Manifold Based Low-Rank Regularization for Image Restoration and Semi-Supervised Learning"],"prefix":"10.1007","volume":"74","author":[{"given":"Rongjie","family":"Lai","sequence":"first","affiliation":[]},{"given":"Jia","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,7,6]]},"reference":[{"key":"492_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-44588-5","volume-title":"Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations","author":"G Aubert","year":"2006","unstructured":"Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, vol. 147. Springer, Berlin (2006)"},{"key":"492_CR2","unstructured":"Bennett, J., Lanning, S.: The Netflix prize. In: Proceedings of KDD cup and workshop, pp. 35. (2007)"},{"key":"492_CR3","doi-asserted-by":"crossref","unstructured":"Bertalmio, M., Sapiro, G., Caselles, V., Ballester, C.: Image inpainting. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, pp. 417\u2013424. ACM Press\/Addison-Wesley Publishing Co., (2000)","DOI":"10.1145\/344779.344972"},{"key":"492_CR4","unstructured":"Buades, A., Coll, B., Morel, J-M.: A non-local algorithm for image denoising. In: Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), vol. 2, pp. 60\u201365. IEEE, (2005)"},{"key":"492_CR5","unstructured":"Buades, A., Coll, B., Morel, J-M.: Image enhancement by non-local reverse heat equation. Preprint CMLA, 22 (2006)"},{"issue":"3","key":"492_CR6","doi-asserted-by":"publisher","first-page":"379","DOI":"10.3934\/ipi.2010.4.379","volume":"4","author":"JF Cai","year":"2010","unstructured":"Cai, J.F., Chan, R.H., Shen, Z.: Simultaneous cartoon and texture inpainting. Inverse Probl. Imaging 4(3), 379\u2013395 (2010)","journal-title":"Inverse Probl. Imaging"},{"issue":"4","key":"492_CR7","doi-asserted-by":"publisher","first-page":"1956","DOI":"10.1137\/080738970","volume":"20","author":"JF Cai","year":"2010","unstructured":"Cai, J.F., Cand\u00e8s, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956\u20131982 (2010)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"492_CR8","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.acha.2007.10.002","volume":"24","author":"JF Cai","year":"2008","unstructured":"Cai, J.F., Chan, R.H., Shen, Z.: A framelet-based image inpainting algorithm. Appl. Comput. Harmon. Anal. 24(2), 131\u2013149 (2008)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"492_CR9","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1007\/s10208-009-9045-5","volume":"9","author":"EJ Cand\u00e8s","year":"2008","unstructured":"Cand\u00e8s, E.J., Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. 9, 717\u2013772 (2008)","journal-title":"Found. Comput. Math."},{"issue":"1","key":"492_CR10","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/s10851-006-6865-7","volume":"26","author":"TF Chan","year":"2006","unstructured":"Chan, T.F., Kang, S.H.: Error analysis for image inpainting. J. Math. Imaging Vis. 26(1), 85\u2013103 (2006)","journal-title":"J. Math. Imaging Vis."},{"issue":"4","key":"492_CR11","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1006\/jvci.2001.0487","volume":"12","author":"TF Chan","year":"2001","unstructured":"Chan, T.F., Shen, J.: Nontexture inpainting by curvature-driven diffusions. J. Vis. Commun. Image Represent. 12(4), 436\u2013449 (2001)","journal-title":"J. Vis. Commun. Image Represent."},{"key":"492_CR12","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717877","volume-title":"Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods","author":"TF Chan","year":"2005","unstructured":"Chan, T.F., Shen, J.: Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. SIAM, Philadelphia (2005)"},{"issue":"1","key":"492_CR13","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/s10851-006-5257-3","volume":"25","author":"TF Chan","year":"2006","unstructured":"Chan, T.F., Shen, J., Zhou, H.M.: Total variation wavelet inpainting. J. Math. Imaging Vis. 25(1), 107\u2013125 (2006)","journal-title":"J. Math. Imaging Vis."},{"key":"492_CR14","doi-asserted-by":"crossref","unstructured":"Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising with block-matching and 3D filtering. In: Electronic Imaging. International Society for Optics and Photonics, (2006)","DOI":"10.1117\/12.643267"},{"issue":"1","key":"492_CR15","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1109\/42.276157","volume":"13","author":"M Defrise","year":"1994","unstructured":"Defrise, M., Clack, R.: A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection. IEEE Trans. Med. Imaging 13(1), 186\u2013195 (1994)","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"2","key":"492_CR16","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1016\/j.acha.2011.06.001","volume":"32","author":"B Dong","year":"2012","unstructured":"Dong, B., Ji, H., Li, J., Shen, Z., Xu, Y.: Wavelet frame based blind image inpainting. Appl. Comput. Harmon. Anal. 32(2), 268\u2013279 (2012)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"2\u20133","key":"492_CR17","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/s10915-012-9579-6","volume":"54","author":"B Dong","year":"2013","unstructured":"Dong, B., Li, J., Shen, Z.: X-ray CT image reconstruction via wavelet frame based regularization and radon domain inpainting. J. Sci. Comput. 54(2\u20133), 333\u2013349 (2013)","journal-title":"J. Sci. Comput."},{"key":"492_CR18","unstructured":"Dong, B., Shen, Z.: Mra-based wavelet frames and applications. In: IAS Lecture Notes Series, Summer Program on \u201cThe Mathematics of Image Processing\u201d, Park City Mathematics Institute, (2010)"},{"issue":"8","key":"492_CR19","doi-asserted-by":"publisher","first-page":"3618","DOI":"10.1109\/TIP.2014.2329449","volume":"23","author":"W Dong","year":"2014","unstructured":"Dong, W., Shi, G., Li, X., Ma, Y., Huang, F.: Compressive sensing via nonlocal low-rank regularization. IEEE Trans. Image Process. 23(8), 3618\u20133632 (2014)","journal-title":"IEEE Trans. Image Process."},{"issue":"6","key":"492_CR20","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1364\/JOSAA.1.000612","volume":"1","author":"LA Feldkamp","year":"1984","unstructured":"Feldkamp, L.A., Davis, L.C., Kress, J.W.: Practical cone-beam algorithm. J. Opt. Soc. Am. A 1(6), 612\u2013619 (1984)","journal-title":"J. Opt. Soc. Am. A"},{"issue":"3","key":"492_CR21","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1137\/070698592","volume":"7","author":"G Gilboa","year":"2008","unstructured":"Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Model. Sim. 7(3), 1005\u20131028 (2008)","journal-title":"Multiscale Model. Sim."},{"issue":"7","key":"492_CR22","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1109\/TIP.2002.800883","volume":"11","author":"G Gilboa","year":"2002","unstructured":"Gilboa, G., Sochen, N., Zeevi, Y.Y.: Forward-and-backward diffusion processes for adaptive image enhancement and denoising. IEEE Trans. Image Process. 11(7), 689\u2013703 (2002)","journal-title":"IEEE Trans. Image Process."},{"issue":"8","key":"492_CR23","doi-asserted-by":"publisher","first-page":"1020","DOI":"10.1109\/TPAMI.2004.47","volume":"26","author":"G Gilboa","year":"2004","unstructured":"Gilboa, G., Sochen, N.A., Zeevi, Y.Y.: Image enhancement and denoising by complex diffusion processes. IEEE Trans. Pattern Anal. Machin. Intell. 26(8), 1020\u20131036 (2004)","journal-title":"IEEE Trans. Pattern Anal. Machin. Intell."},{"key":"492_CR24","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970838","volume-title":"Augmented Lagrangian and Operator-splitting Methods in Nonlinear Mechanics","author":"R Glowinski","year":"1989","unstructured":"Glowinski, R., Le Tallec, P.: Augmented Lagrangian and Operator-splitting Methods in Nonlinear Mechanics. SIAM, Philadelphia (1989)"},{"issue":"2","key":"492_CR25","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1137\/080725891","volume":"2","author":"T Goldstein","year":"2009","unstructured":"Goldstein, T., Osher, S.: The split bregman method for l1-regularized problems. SIAM J. Imaging Sci. 2(2), 323\u2013343 (2009)","journal-title":"SIAM J. Imaging Sci."},{"issue":"3","key":"492_CR26","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1016\/0022-5193(70)90109-8","volume":"29","author":"R Gordon","year":"1970","unstructured":"Gordon, R., Bender, R., Herman, G.T.: Algebraic Reconstruction Techniques (ART) for three-dimensional electron microscopy and X-ray photography. J. Theor. Biol. 29(3), 471\u2013481 (1970)","journal-title":"J. Theor. Biol."},{"key":"492_CR27","volume-title":"Computed Tomography: Principles, Design, Artifacts and Recent Advances","author":"Jiang Hsieh","year":"2003","unstructured":"Hsieh, Jiang: Computed Tomography: Principles, Design, Artifacts and Recent Advances, vol. 114. SPIE press, Bellingham (2003)"},{"issue":"13","key":"492_CR28","doi-asserted-by":"publisher","first-page":"3787","DOI":"10.1088\/0031-9155\/56\/13\/004","volume":"56","author":"X Jia","year":"2011","unstructured":"Jia, X., Dong, B., Lou, Y., Jiang, S.B.: GPU-based iterative cone beam CT reconstruction using tight frame regularization. Phys. Med. Biol. 56(13), 3787 (2011)","journal-title":"Phys. Med. Biol."},{"issue":"2","key":"492_CR29","doi-asserted-by":"crossref","first-page":"139","DOI":"10.3233\/XST-2011-0283","volume":"19","author":"X Jia","year":"2011","unstructured":"Jia, X., Lou, Y., Lewis, J., Li, R., Gu, X., Men, C., Jiang, S.B.: GPU-based fast low-dose cone beam CT reconstruction via total variation. J. X-ray Sci. Technol. 19(2), 139\u2013153 (2011)","journal-title":"J. X-ray Sci. Technol."},{"key":"492_CR30","unstructured":"Kuang, D., Shi, Z., Osher, S., Bertozzi, A.: A harmonic extension approach for collaborative ranking. \n                    arXiv:1602.05127\n                    \n                  , (2016)"},{"issue":"11","key":"492_CR31","doi-asserted-by":"publisher","first-page":"2278","DOI":"10.1109\/5.726791","volume":"86","author":"Y LeCun","year":"1998","unstructured":"LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278\u20132324 (1998)","journal-title":"Proc. IEEE"},{"issue":"21","key":"492_CR32","doi-asserted-by":"publisher","first-page":"5643","DOI":"10.1088\/0031-9155\/51\/21\/017","volume":"51","author":"L Li","year":"2006","unstructured":"Li, L., Chen, Z., Xing, Y., Zhang, L., Kang, K., Wang, G.: A general exact method for synthesizing parallel-beam projections from cone-beam projections via filtered backprojection. Phys. Med. Biol. 51(21), 5643\u20135654 (2006)","journal-title":"Phys. Med. Biol."},{"issue":"1","key":"492_CR33","doi-asserted-by":"publisher","first-page":"228","DOI":"10.4208\/cicp.111015.250716a","volume":"22","author":"Z Li","year":"2017","unstructured":"Li, Z., Shi, Z., Sun, J.: Point integral method for solving poisson-type equations on manifolds from point clouds with convergence guarantees. Commun. Comput. Phys. 22(1), 228\u2013258 (2017)","journal-title":"Commun. Comput. Phys."},{"issue":"3","key":"492_CR34","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0165-1684(96)00042-4","volume":"51","author":"F Noo","year":"1996","unstructured":"Noo, F., Bernard, C., Litt, F.X., Marchot, P.: A comparison between filtered backprojection algorithm and direct algebraic method in fan beam CT. Signal Process. 51(3), 191\u2013199 (1996)","journal-title":"Signal Process."},{"key":"492_CR35","doi-asserted-by":"crossref","unstructured":"Osher, S., Shi, Z., Zhu, W.: Low dimensional manifold model for image processing. SIAM J. Imaging Sci. (to appear, 2017)","DOI":"10.1137\/16M1058686"},{"issue":"2","key":"492_CR36","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/j.cviu.2008.09.003","volume":"113","author":"G Peyr\u00e9","year":"2009","unstructured":"Peyr\u00e9, G.: Manifold models for signals and images. Comput. Vis. Image Underst. 113(2), 249\u2013260 (2009)","journal-title":"Comput. Vis. Image Underst."},{"issue":"2","key":"492_CR37","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s10915-014-9893-2","volume":"63","author":"Y Quan","year":"2015","unstructured":"Quan, Y., Ji, H., Shen, Z.: Data-driven multi-scale non-local wavelet frame construction and image recovery. J. Sci. Comput. 63(2), 307\u2013329 (2015)","journal-title":"J. Sci. Comput."},{"key":"492_CR38","first-page":"262","volume":"69","author":"J Radon","year":"1917","unstructured":"Radon, J.: \u00dcber die Bestimmung von Funktionen durch ihre Integralwerte l\u00e4ngs gewisser Mannigfaltigkeiten. Berichte S\u00e4chsische Akademie der Wissenschaften 69, 262\u2013267 (1917)","journal-title":"Berichte S\u00e4chsische Akademie der Wissenschaften"},{"key":"492_CR39","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"L Rudin","year":"1992","unstructured":"Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60, 259\u2013268 (1992)","journal-title":"Phys. D"},{"issue":"3","key":"492_CR40","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1137\/S0036139900368844","volume":"62","author":"J Shen","year":"2002","unstructured":"Shen, J., Chan, T.F.: Mathematical models for local nontexture inpaintings. SIAM J. Appl. Math. 62(3), 1019\u20131043 (2002)","journal-title":"SIAM J. Appl. Math."},{"key":"492_CR41","unstructured":"Shi, Z., Osher, S., Zhu, W.: Low dimensional manifold model with semi-local patches. UCLA CAM Report (16\u201363) (2016)"},{"key":"492_CR42","unstructured":"Shi, Z., Osher, S., Zhu, W.: Weighted graph laplacian and image inpainting. J. Sci. Comput. 577 (to appear, 2017)"},{"key":"492_CR43","unstructured":"Shi, Z., Sun, J., Tian, M.: Harmonic extension. \n                    arXiv:1509.06458\n                    \n                  , (2015)"},{"key":"492_CR44","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1118\/1.595715","volume":"12","author":"RL Siddon","year":"1985","unstructured":"Siddon, R.L.: Fast calculation of the exact radiological path for a 3-dimensional CT array. Med. Phys. 12, 252\u2013255 (1985)","journal-title":"Med. Phys."},{"issue":"1","key":"492_CR45","doi-asserted-by":"publisher","first-page":"191","DOI":"10.3934\/ipi.2010.4.191","volume":"4","author":"X Zhang","year":"2010","unstructured":"Zhang, X., Chan, T.F.: Wavelet inpainting by nonlocal total variation. Inverse Probl. Imaging 4(1), 191\u2013210 (2010)","journal-title":"Inverse Probl. Imaging"},{"key":"492_CR46","first-page":"912","volume":"3","author":"X Zhu","year":"2003","unstructured":"Zhu, X., Ghahramani, Z., Lafferty, J.: Semi-supervised learning using gaussian fields and harmonic functions. ICML 3, 912\u2013919 (2003)","journal-title":"ICML"},{"issue":"1","key":"492_CR47","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2200\/S00196ED1V01Y200906AIM006","volume":"3","author":"X Zhu","year":"2009","unstructured":"Zhu, X., Goldberg, A.B.: Introduction to semi-supervised learning. Synth. Lect. Artif. Intell. Machin. Learn. 3(1), 1\u2013130 (2009)","journal-title":"Synth. Lect. Artif. Intell. Machin. Learn."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0492-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0492-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0492-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T09:22:19Z","timestamp":1589707339000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0492-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,6]]},"references-count":47,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,3]]}},"alternative-id":["492"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0492-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,6]]},"assertion":[{"value":"12 April 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 June 2017","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 June 2017","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 July 2017","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}