{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T01:21:19Z","timestamp":1792200079759,"version":"4.4.0"},"reference-count":67,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>Algorithms based on total variation (TV) minimization are prevalent in image processing. They play a key role in a variety of applications such as image denoising, compressive sensing, and inverse problems in general. In this work, we extend the TV dual framework that includes Chambolle's and Gilboa and Osher's projection algorithms for TV minimization. We use a flexible graph data representation that allows us to generalize the constraint on the projection variable. We show how this new formulation of the TV problem may be solved by means of fast parallel proximal algorithms. In denoising and deblurring examples, the proposed approach is shown not only to perform better than recent TV-based approaches, but also to perform well on arbitrary graphs instead of regular grids. The proposed method consequently applies to a variety of other inverse problems including image fusion and mesh filtering.<\/jats:p>","DOI":"10.1137\/120895068","type":"journal-article","created":{"date-parts":[[2013,7,11]],"date-time":"2013-07-11T10:32:21Z","timestamp":1373538741000},"page":"1246-1273","source":"Crossref","is-referenced-by-count":67,"title":["Dual Constrained TV-based Regularization on Graphs"],"prefix":"10.1137","volume":"6","author":[{"given":"Camille","family":"Couprie","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leo","family":"Grady","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laurent","family":"Najman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Christophe","family":"Pesquet","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hugues","family":"Talbot","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,7,11]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2010.2076294"},{"key":"atypb2","unstructured":"K. J. Arrow, L. Hurwicz, and H. Uzawa,<i>Studies in Linear and Non-linear Programming<\/i> Stanford University Press, Stanford, CA, 1958."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-009-0149-y"},{"key":"atypb4","first-page":"1469","author":"Bagnato L.","year":"2009","journal-title":"Egypt"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"H. H. Bauschke and P. L. Combettes,<i>Convex Analysis and Monotone Operator Theory in Hilbert Spaces<\/i> Springer, New York, 2011.","DOI":"10.1007\/978-1-4419-9467-7"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"atypb7","first-page":"128","author":"Bougleux S.","year":"2007","journal-title":"Italy"},{"key":"atypb8","first-page":"28","author":"Boyle J. P.","year":"1986","journal-title":"Berlin"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994273343"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/090769521"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2012.08.053"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1145\/359094.359101"},{"key":"atypb13","unstructured":"X. Bresson,<i>A Short Note for Nonlocal TV Minimization<\/i> 2009, http:\/\/www.cs.cityu.edu.hk\/$\\!_{^{\\sim}}\\!$xbresson\/ codes_files\/xbresson_2009_short_note_nonlocal_TV_minimization.pdf."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/10081602X"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"A. Buades, B. Coll, and J.M. Morel,<i>A non-local algorithm for image denoising<\/i> in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Vol. 2, San Diego, CA, 2005, pp. 60-65.","DOI":"10.1109\/CVPR.2005.38"},{"key":"atypb16","unstructured":"J. Carter,<i>Dual Methods for Total Variation-based Image Restoration<\/i> Ph.D. thesis, UCLA, Los Angeles, CA, 2002."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1023\/B:JMIV.0000011325.36760.1e"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-009-0238-9"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050258"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-010-0251-1"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596299767"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1109\/83.902288"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582566"},{"key":"atypb24","first-page":"465","author":"Ciril I.","year":"2011","journal-title":"Heidelberg"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-010-0147-7"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2004.832922"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1137\/060669498"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/24\/6\/065014"},{"key":"atypb29","first-page":"185","author":"Combettes P. L.","year":"2010","journal-title":"New York"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1007\/s11228-011-0191-y"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1155\/2008\/590183"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1137\/100799186"},{"key":"atypb33","first-page":"945","author":"Couprie C.","year":"2011","journal-title":"Czech Republic"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-006-8803-0"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.1983.1143132"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2008.924284"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20045"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1137\/09076934X"},{"key":"atypb39","unstructured":"M. Fortin and R. Glowinski, eds.<i>Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems<\/i> North-Holland, Amsterdam, 1983."},{"key":"atypb40","unstructured":"G. Gilboa, J. Darbon, S. Osher, and T. Chan,<i>Nonlocal Convex Functionals for Image Regularization<\/i> UCLA CAM Report 06-57, UCLA, Los Angeles, CA, 2006."},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1137\/060669358"},{"key":"atypb42","doi-asserted-by":"crossref","unstructured":"R. Glowinski and P. L. Tallec,<i>Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics<\/i> SIAM Stud. Appl. Math. 9, SIAM, Philadelphia, 1989.","DOI":"10.1137\/1.9781611970838"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1137\/080725891"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2009.2028258"},{"key":"atypb45","unstructured":"L. Grady and E. L. Schwartz,<i>The Graph Analysis Toolbox: Image Processing on Arbitrary Graphs<\/i> Technical Report CAS\/CNS-TR-03-021, Department of Cognitive and Neural Systems, Boston University, Boston, MA, 2003."},{"key":"atypb46","unstructured":"L. J. Grady,<i>Space-Variant Computer Vision: A Graph-Theoretic Approach<\/i> Ph.D. thesis, Boston University, Boston, MA, 2004."},{"key":"atypb47","unstructured":"L. J. Grady and J. R. Polimeni,<i>Discrete Calculus: Applied Analysis on Graphs for Computational Science<\/i> Springer-Verlag, London, 2010."},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-012-0348-9"},{"key":"atypb49","unstructured":"A. N. Hirani,<i>Discrete Exterior Calculus<\/i> Ph.D. thesis, California Institute of Technology, Pasadena, CA, 2003."},{"key":"atypb50","first-page":"368","author":"Jalalzai K.","year":"2009","journal-title":"Heidelberg"},{"key":"atypb51","first-page":"2297","volume":"12","author":"Jenatton R.","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"atypb52","doi-asserted-by":"crossref","unstructured":"F. Lenzen, F. Becker, J. Lellmann, S. Petra, and C. Schn\u00f6rr,<i>Variational image denoising with adaptive constraint sets<\/i> in Scale Space and Variational Methods in Computer Vision, A. M. Bruckstein, B. M. ter Haar Romeny, A. M. Bronstein, and M. M. Bronstein, eds., Lecture Notes in Comput. Sci. 6667, Springer, Berlin, Heidelberg, 2011, pp. 206-217.","DOI":"10.1007\/978-3-642-24785-9_18"},{"key":"atypb53","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-012-9456-0"},{"key":"atypb54","unstructured":"O. L\u00e9zoray and L. Grady, eds.<i>Image Processing and Analysis with Graphs: Theory and Practice<\/i> Digital Imaging and Computer Vision, CRC Press\/Taylor and Francis, Boca Raton, FL, 2012."},{"key":"atypb55","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2002.806241"},{"key":"atypb56","doi-asserted-by":"crossref","unstructured":"Y. Meyer,<i>Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures<\/i> American Mathematical Society, Providence, RI, 2001.","DOI":"10.1090\/ulect\/022"},{"key":"atypb57","doi-asserted-by":"publisher","DOI":"10.1137\/040605412"},{"key":"atypb58","first-page":"273","volume":"8","author":"Pesquet J.-C.","year":"2012","journal-title":"Pac. J. Optim."},{"key":"atypb59","first-page":"792","author":"Pock T.","year":"2008","journal-title":"Heidelberg"},{"key":"atypb60","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2011.2128335"},{"key":"atypb61","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.21012"},{"key":"atypb62","unstructured":"R. T. Rockafellar,<i>Convex Analysis<\/i> Princeton Landmarks Math., Princeton University Press, Princeton, NJ, 1997."},{"key":"atypb63","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90242-F"},{"key":"atypb64","doi-asserted-by":"publisher","DOI":"10.1016\/j.jvcir.2009.10.006"},{"key":"atypb65","first-page":"283","author":"Taubin G.","year":"1996","journal-title":"Heidelberg"},{"key":"atypb66","doi-asserted-by":"publisher","DOI":"10.1137\/080714488"},{"key":"atypb67","doi-asserted-by":"publisher","DOI":"10.1137\/090746379"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/120895068","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:25:40Z","timestamp":1787322340000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/120895068"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1]]},"references-count":67,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["10.1137\/120895068"],"URL":"https:\/\/doi.org\/10.1137\/120895068","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1]]}}}