{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T08:37:52Z","timestamp":1785487072543,"version":"3.56.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2010,12,21]],"date-time":"2010-12-21T00:00:00Z","timestamp":1292889600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2011,5]]},"DOI":"10.1007\/s10851-010-0251-1","type":"journal-article","created":{"date-parts":[[2010,12,20]],"date-time":"2010-12-20T16:27:47Z","timestamp":1292862467000},"page":"120-145","source":"Crossref","is-referenced-by-count":3405,"title":["A First-Order Primal-Dual Algorithm for Convex Problems with\u00a0Applications to Imaging"],"prefix":"10.1007","volume":"40","author":[{"given":"Antonin","family":"Chambolle","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"Pock","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2010,12,21]]},"reference":[{"key":"251_CR1","volume-title":"Stanford Mathematical Studies in the Social Sciences","author":"K.J. Arrow","year":"1958","unstructured":"Arrow, K.J., Hurwicz, L., Uzawa, H.: Studies in linear and non-linear programming. In: Chenery, H.B., Johnson, S.M., Karlin, S., Marschak, T., Solow, R.M. (eds.) Stanford Mathematical Studies in the Social Sciences, vol.\u00a0II. Stanford University Press, Stanford (1958)"},{"issue":"1","key":"251_CR2","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A. Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183\u2013202 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"251_CR3","series-title":"Lecture Notes in Statist.","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1007\/978-1-4613-9940-7_3","volume-title":"Advances in Order Restricted Statistical Inference","author":"J.P. Boyle","year":"1986","unstructured":"Boyle, J.P., Dykstra, R.L.: A method for finding projections onto the intersection of convex sets in Hilbert spaces. In: Advances in Order Restricted Statistical Inference, Iowa City, Iowa, 1985. Lecture Notes in Statist., vol. 37, pp. 28\u201347. Springer, Berlin (1986)"},{"issue":"4","key":"251_CR4","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/BF02921771","volume":"5","author":"K.A. Brakke","year":"1995","unstructured":"Brakke, K.A.: Soap films and covering spaces. J. Geom. Anal. 5(4), 445\u2013514 (1995)","journal-title":"J. Geom. Anal."},{"issue":"3","key":"251_CR5","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1137\/05064182X","volume":"5","author":"E. Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E., Demanet, L., Donoho, D., Ying, L.: Fast discrete curvelet transforms. Multiscale Model. Simul. 5(3), 861\u2013899 (2006) (electronic)","journal-title":"Multiscale Model. Simul."},{"issue":"1\u20132","key":"251_CR6","first-page":"89","volume":"20","author":"A. Chambolle","year":"2004","unstructured":"Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20(1\u20132), 89\u201397 (2004). Special issue on mathematics and image analysis","journal-title":"J. Math. Imaging Vis."},{"key":"251_CR7","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1007\/11585978_10","volume-title":"Energy Minimization Methods in Computer Vision and Pattern Recognition","author":"A. Chambolle","year":"2005","unstructured":"Chambolle, A.: Total variation minimization and a class of binary MRF models. In: Energy Minimization Methods in Computer Vision and Pattern Recognition, pp. 136\u2013152 (2005)"},{"key":"251_CR8","unstructured":"Chambolle, A., Cremers, D., Pock, T.: A convex approach for computing minimal partitions. Technical Report 649, CMAP, Ecole Polytechnique, France (2008)"},{"key":"251_CR9","doi-asserted-by":"crossref","unstructured":"Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. http:\/\/hal.archives-ouvertes.fr\/hal-00490826 (2010)","DOI":"10.1007\/s10851-010-0251-1"},{"issue":"3","key":"251_CR10","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/BF01581204","volume":"55","author":"J. Eckstein","year":"1992","unstructured":"Eckstein, J., Bertsekas, D.P.: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program., Ser. A 55(3), 293\u2013318 (1992)","journal-title":"Math. Program., Ser. A"},{"key":"251_CR11","unstructured":"Esser, E.: Applications of Lagrangian-based alternating direction methods and connections to split Bregman. CAM Reports 09-31, UCLA, Center for Applied Math. (2009)"},{"key":"251_CR12","unstructured":"Esser, E., Zhang, X., Chan, T.: A general framework for a class of first order primal-dual algorithms for tv minimization. CAM Reports 09-67, UCLA, Center for Applied Math. (2009)"},{"key":"251_CR13","doi-asserted-by":"crossref","unstructured":"Fadili, J., Peyr\u00e9, G.: Total variation projection with first order schemes. http:\/\/hal.archives-ouvertes.fr\/hal-00380491\/ (2009)","DOI":"10.1109\/ICIP.2009.5413571"},{"issue":"1","key":"251_CR14","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/MCSE.2010.14","volume":"12","author":"J. Fadili","year":"2010","unstructured":"Fadili, J., Starck, J.-L., Elad, M., Donoho, D.: Mcalab: Reproducible research in signal and image decomposition and inpainting. Comput. Sci. Eng. 12(1), 44\u201363 (2010)","journal-title":"Comput. Sci. Eng."},{"key":"251_CR15","unstructured":"Goldstein, T., Osher, S.: The split Bregman algorithm for l1 regularized problems. CAM Reports 08-29, UCLA, Center for Applied Math. (2008)"},{"key":"251_CR16","unstructured":"He, B., Yuan, X.: Convergence analysis of primal-dual algorithms for total variation image restoration. Technical Report 2790, Optimization Online, November 2010 (available at www.optimization-online.org )"},{"issue":"4","key":"251_CR17","first-page":"747","volume":"12","author":"G.M. Korpelevi\u010d","year":"1976","unstructured":"Korpelevi\u010d, G.M.: An extragradient method for finding saddle points and for other problems. \u00c8kon. Mat. Metody 12(4), 747\u2013756 (1976)","journal-title":"\u00c8kon. Mat. Metody"},{"issue":"1","key":"251_CR18","doi-asserted-by":"crossref","first-page":"55","DOI":"10.2140\/pjm.1994.166.55","volume":"166","author":"G. Lawlor","year":"1994","unstructured":"Lawlor, G., Morgan, F.: Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms. Pac. J. Math. 166(1), 55\u201383 (1994)","journal-title":"Pac. J. Math."},{"issue":"6","key":"251_CR19","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1137\/0716071","volume":"16","author":"P.-L. Lions","year":"1979","unstructured":"Lions, P.-L., Mercier, B.: Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16(6), 964\u2013979 (1979)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"251_CR20","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/BF00938486","volume":"50","author":"C. Michelot","year":"1986","unstructured":"Michelot, C.: A finite algorithm for finding the projection of a point onto the canonical simplex of R n . J. Optim. Theory Appl. 50(1), 195\u2013200 (1986)","journal-title":"J. Optim. Theory Appl."},{"key":"251_CR21","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1002\/cpa.3160420503","volume":"42","author":"D. Mumford","year":"1989","unstructured":"Mumford, D., Shah, J.: Optimal approximation by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42, 577\u2013685 (1989)","journal-title":"Commun. Pure Appl. Math."},{"issue":"1","key":"251_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10957-009-9539-y","volume":"142","author":"A. Nedi\u0107","year":"2009","unstructured":"Nedi\u0107, A., Ozdaglar, A.: Subgradient methods for saddle-point problems. J. Optim. Theory Appl. 142(1), 1 (2009)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"251_CR23","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1137\/S1052623403425629","volume":"15","author":"A. Nemirovski","year":"2004","unstructured":"Nemirovski, A.: Prox-method with rate of convergence O(1\/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J. Optim. 15(1), 229\u2013251 (2004) (electronic)","journal-title":"SIAM J. Optim."},{"key":"251_CR24","series-title":"A Wiley-Interscience Publication","volume-title":"Problem Complexity and Method Efficiency in Optimization","author":"A. Nemirovski","year":"1983","unstructured":"Nemirovski, A., Yudin, D.: Problem Complexity and Method Efficiency in Optimization. A Wiley-Interscience Publication. Wiley, New York (1983). Translated from the Russian and with a preface by E.R. Dawson, Wiley-Interscience Series in Discrete Mathematics"},{"issue":"3","key":"251_CR25","first-page":"543","volume":"269","author":"Yu. Nesterov","year":"1983","unstructured":"Nesterov, Yu.: A method for solving the convex programming problem with convergence rate O(1\/k 2). Dokl. Akad. Nauk SSSR 269(3), 543\u2013547 (1983)","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"251_CR26","series-title":"Applied Optimization","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8853-9","volume-title":"Introductory Lectures on Convex Optimization","author":"Yu. Nesterov","year":"2004","unstructured":"Nesterov, Yu.: Introductory Lectures on Convex Optimization. Applied Optimization, vol.\u00a087. Kluwer Academic, Boston (2004). A basic course"},{"issue":"1","key":"251_CR27","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10107-004-0552-5","volume":"103","author":"Yu. Nesterov","year":"2005","unstructured":"Nesterov, Yu.: Smooth minimization of non-smooth functions. Math. Program., Ser. A 103(1), 127\u2013152 (2005)","journal-title":"Math. Program., Ser. A"},{"key":"251_CR28","unstructured":"Nesterov, Yu.: Gradient methods for minimizing composite objective function. Technical report, CORE DISCUSSION PAPER (2007)"},{"key":"251_CR29","series-title":"LNCS","volume-title":"ICCV Proceedings","author":"T. Pock","year":"2009","unstructured":"Pock, T., Cremers, D., Bischof, H., Chambolle, A.: An algorithm for minimizing the Mumford-Shah functional. In: ICCV Proceedings, LNCS. Springer, Berlin (2009)"},{"issue":"5","key":"251_CR30","first-page":"777","volume":"28","author":"L.D. Popov","year":"1980","unstructured":"Popov, L.D.: A modification of the Arrow-Hurwitz method of search for saddle points. Mat. Zametki 28(5), 777\u2013784, 803 (1980)","journal-title":"Mat. Zametki"},{"issue":"5","key":"251_CR31","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"R.T. Rockafellar","year":"1976","unstructured":"Rockafellar, R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14(5), 877\u2013898 (1976)","journal-title":"SIAM J. Control Optim."},{"key":"251_CR32","series-title":"Princeton Landmarks in Mathematics","volume-title":"Convex Analysis","author":"R.T. Rockafellar","year":"1997","unstructured":"Rockafellar, R.T.: Convex Analysis, Princeton Landmarks in Mathematics. Princeton University Press, Princeton (1997). Reprint of the 1970 original, Princeton Paperbacks"},{"key":"251_CR33","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"L. Rudin","year":"1992","unstructured":"Rudin, L., Osher, S.J., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259\u2013268 (1992) [also in Experimental Mathematics: Computational Issues in Nonlinear Science (Proc. Los Alamos Conf. 1991)]","journal-title":"Physica D"},{"key":"251_CR34","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1109\/WVM.1989.47097","volume-title":"Proceedings Workshop on Visual Motion","author":"D. Shulman","year":"1989","unstructured":"Shulman, D., Herv\u00e9, J.-Y.: Regularization of discontinuous flow fields. In: Proceedings Workshop on Visual Motion, pp. 81\u201386 (1989)"},{"key":"251_CR35","first-page":"243","volume-title":"Vision, Modeling, and Visualization 2008","author":"C. Zach","year":"2008","unstructured":"Zach, C., Gallup, D., Frahm, J.M., Niethammer, M.: Fast global labeling for real-time stereo using multiple plane sweeps. In: Vision, Modeling, and Visualization 2008, pp. 243\u2013252. IOS Press, Amsterdam (2008)"},{"key":"251_CR36","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1007\/978-3-540-74936-3_22","volume-title":"29th DAGM Symposium on Pattern Recognition","author":"C. Zach","year":"2007","unstructured":"Zach, C., Pock, T., Bischof, H.: A duality based approach for realtime TV-L 1 optical flow. In: 29th DAGM Symposium on Pattern Recognition, pp.\u00a0214\u2013223. Heidelberg, Germany (2007)"},{"key":"251_CR37","unstructured":"Zhu, M., Chan, T.: An efficient primal-dual hybrid gradient algorithm for total variation image restoration. CAM Reports 08-34, UCLA, Center for Applied Math. (2008)"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-010-0251-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-010-0251-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-010-0251-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T06:09:47Z","timestamp":1559887787000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-010-0251-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12,21]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,5]]}},"alternative-id":["251"],"URL":"https:\/\/doi.org\/10.1007\/s10851-010-0251-1","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,12,21]]}}}