{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:29:10Z","timestamp":1787318950195,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>In this article we study a continuous primal-dual method proposed by Appleton and Talbot and generalize it to other problems in image processing. We interpret it as an Arrow\u2013Hurwicz method which leads to a better description of the system of PDEs obtained. We show existence and uniqueness of solutions and get a convergence result for the denoising problem. Our analysis also yields new a posteriori estimates.<\/jats:p>","DOI":"10.1137\/100789178","type":"journal-article","created":{"date-parts":[[2011,3,24]],"date-time":"2011-03-24T18:16:24Z","timestamp":1300990584000},"page":"366-385","source":"Crossref","is-referenced-by-count":1,"title":["Continuous Primal-Dual Methods for Image Processing"],"prefix":"10.1137","volume":"4","author":[{"given":"M.","family":"Goldman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,3,24]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"L. Ambrosio, N. Fusco, and D. Pallara,\n                      Functions of Bounded Variation and Free Discontinuity Problems\n                      , Oxford Science Publications, Oxford, UK, 2000.","DOI":"10.1093\/oso\/9780198502456.001.0001"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"F. Andreu-Vaillo, V. Caselles, and J. M. 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Cremers, and T. Pock,\n                      An introduction to total variation for image analysis\n                      , in Theoretical Foundations and Numerical Methods for Sparse Recovery, M. Fornassier, ed., DeGruyter, Berlin, 2010.","DOI":"10.1515\/9783110226157.263"},{"key":"R9","unstructured":"A. Chambolle, D. Cremers, and T. Pock,\n                      A Convex Approach for Computing Minimal Partitions\n                      , CMAP technical report, 2008."},{"key":"R10","unstructured":"A. Chambolle, S. E. Levine, and B. J. Lucier,\n                      Some Variations on Total Variation-Based Image Smoothing\n                      , preprint, 2009."},{"key":"R11","doi-asserted-by":"crossref","unstructured":"A. Chambolle and T. 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Rockafellar,\n                      Monotone operators associated with saddle-functions and minimax problems\n                      , in Nonlinear Functional Analysis, Proceedings of the Symposium in Pure Mathematics of the American Mathematics Society, F. E. Browder, ed., 1968, Vol. XVIII, pp. 241\u2013250.","DOI":"10.1090\/pspum\/018.1\/0285942"},{"key":"R20","unstructured":"M. Zhu and T. Chan,\n                      An Efficient Primal-Dual Hybrid Gradient Algorithm for Total Variation Image Restoration\n                      , CAM Report 08-34, Center for Applied Math., UCLA, Los Angeles, CA, 2008."}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100789178","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:43:43Z","timestamp":1787316223000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100789178"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1137\/100789178"],"URL":"https:\/\/doi.org\/10.1137\/100789178","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1]]}}}