{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:35:47Z","timestamp":1772296547717,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2008,9,24]],"date-time":"2008-09-24T00:00:00Z","timestamp":1222214400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2009,10]]},"DOI":"10.1007\/s10444-008-9101-8","type":"journal-article","created":{"date-parts":[[2008,9,23]],"date-time":"2008-09-23T10:49:37Z","timestamp":1222166977000},"page":"237-266","source":"Crossref","is-referenced-by-count":16,"title":["A primal-dual active-set algorithm for bilaterally constrained total variation deblurring and piecewise constant Mumford-Shah segmentation problems"],"prefix":"10.1007","volume":"31","author":[{"given":"D.","family":"Krishnan","sequence":"first","affiliation":[]},{"given":"Quang Vinh","family":"Pham","sequence":"additional","affiliation":[]},{"given":"Andy M.","family":"Yip","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,9,24]]},"reference":[{"issue":"2","key":"9101_CR1","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1137\/0320018","volume":"20","author":"D.P. Bertsekas","year":"1982","unstructured":"Bertsekas, D.P.: Projected Newton methods for optimization problems with simple constraints. SIAM J. Control Optim. 20(2), 221\u2013246 (1982)","journal-title":"SIAM J. Control Optim."},{"key":"9101_CR2","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"S. Boyd","year":"2004","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)"},{"key":"9101_CR3","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/ICCV.2003.1238310","volume-title":"Proceedings of IEEE Intl. Conf. on Computer Vision","author":"Y. Boykov","year":"2003","unstructured":"Boykov, Y., Kolmogorov, V.: Computing geodesics and minimal surfaces via graph cuts. In: Proceedings of IEEE Intl. Conf. on Computer Vision, pp. 26\u201333. IEEE, Piscataway (2003)"},{"key":"9101_CR4","doi-asserted-by":"crossref","first-page":"1124","DOI":"10.1109\/TPAMI.2004.60","volume":"26","author":"Y. Boykov","year":"2004","unstructured":"Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut\/max-flow algorithms for energy minimization in vision. IEEE Trans. Pattern Anal. Mach. Intell. 26, 1124\u20131137 (2004)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"2","key":"9101_CR5","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/s10851-007-0002-0","volume":"28","author":"X. Bresson","year":"2007","unstructured":"Bresson, X., Esedo\u1e21lu, S., Vandergheynst, P., Thiran, J.-P., Osher, S.: Fast global minimization of the active contour\/snake model. J. Math. Imaging Vision. 28(2), 151\u2013167 (2007)","journal-title":"J. Math. Imaging Vision."},{"key":"9101_CR6","unstructured":"Carter, J.L.: Dual methods for total variation-based image restoration. PhD thesis, UCLA, April (2002)"},{"key":"9101_CR7","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1023\/B:JMIV.0000011320.81911.38","volume":"20","author":"A. Chambolle","year":"2004","unstructured":"Chambolle, A.: An algorithm for total variation minimization and applications. J. Math. Imaging Vision 20, 89\u201397 (2004)","journal-title":"J. Math. Imaging Vision"},{"key":"9101_CR8","doi-asserted-by":"crossref","first-page":"1632","DOI":"10.1137\/040615286","volume":"66","author":"T.F. Chan","year":"2006","unstructured":"Chan, T.F., Esedo\u1e21lu, S., Nikolova, M.: Algorithms for finding global minimizers of image segmentation and denoising models. SIAM J. Appl. Math. 66, 1632\u20131648 (2006)","journal-title":"SIAM J. Appl. Math."},{"issue":"6","key":"9101_CR9","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1137\/S1064827596299767","volume":"20","author":"T.F. Chan","year":"1999","unstructured":"Chan, T.F., Golub, G.H., Mulet, P.: A nonlinear primal-dual method for total variation-based image restoration. SIAM J. Sci. Comput. 20(6), 1964\u20131977 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"9101_CR10","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717877","volume-title":"Image Processing and Analysis: Variational, PDE Wavelet, and Stochastic Methods","author":"T.F. Chan","year":"2005","unstructured":"Chan, T.F., Shen, J.: Image Processing and Analysis: Variational, PDE Wavelet, and Stochastic Methods. SIAM, Philadelphia (2005)"},{"key":"9101_CR11","first-page":"14","volume":"50","author":"T.F. Chan","year":"2003","unstructured":"Chan, T.F., Shen, J., Vese, L.: Variational PDE models in image processing. Notices Amer. Math. Soc. 50, 14\u201326 (2003)","journal-title":"Notices Amer. Math. Soc."},{"issue":"2","key":"9101_CR12","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/83.902291","volume":"10","author":"T.F. Chan","year":"2001","unstructured":"Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266\u2013277 (2001)","journal-title":"IEEE Trans. Image Process."},{"key":"9101_CR13","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/s10851-006-8803-0","volume":"26","author":"J. Darbon","year":"2006","unstructured":"Darbon, J., Sigelle, M.: Image restoration with discrete constrained total variation part 1: fast and exact optimization. J. Math. Imaging Vision 26, 261\u2013276 (2006)","journal-title":"J. Math. Imaging Vision"},{"issue":"3","key":"9101_CR14","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1137\/S1052623401383558","volume":"13","author":"M. Hinterm\u00fcller","year":"2003","unstructured":"Hinterm\u00fcller, M., Ito, K., Kunisch, K.: The primal-dual active set strategy as a semismooth Newton\u2019s method. SIAM J. Optim. 13(3), 865\u2013888 (2003)","journal-title":"SIAM J. Optim."},{"key":"9101_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/040613263","volume":"28","author":"M. Hinterm\u00fcller","year":"2006","unstructured":"Hinterm\u00fcller, M., Stadler, G.: A primal-dual algorithm for TV-based inf-convolution-type image restoration. SIAM J. Sci. Comput. 28, 1\u201323 (2006)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"9101_CR16","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/s11263-006-6849-5","volume":"69","author":"O. Juan","year":"2006","unstructured":"Juan, O., Keriven, R., Postelnicu, G.: Stochastic motion and the level set method in computer vision: stochastic active contours. Int. J. Comput. Vision 69(1), 7\u201325 (2006)","journal-title":"Int. J. Comput. Vision"},{"issue":"11","key":"9101_CR17","doi-asserted-by":"crossref","first-page":"2766","DOI":"10.1109\/TIP.2007.908079","volume":"16","author":"D. Krishnan","year":"2007","unstructured":"Krishnan, D., Lin, P., Yip, A.M.: A primal-dual active-set method for non-negativity constrained total variation deblurring problems. IEEE Trans. Image Process. 16(11), 2766\u20132777 (2007)","journal-title":"IEEE Trans. Image Process."},{"key":"9101_CR18","unstructured":"Law, Y.N., Lee, H.K., Yip, A.M.: A multi-resolution stochastic level set method for Mumford-Shah image segmentation. IEEE Trans. Image Process. (2008, in press)"},{"key":"9101_CR19","doi-asserted-by":"crossref","first-page":"1852","DOI":"10.1137\/030601272","volume":"26","author":"F. Lin","year":"2005","unstructured":"Lin, F., Ng, M., Ching, W.: Factorized banded inverse preconditioners for matrices with Toeplitz structure. SIAM J. Sci. Comput. 26, 1852\u20131870 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"9101_CR20","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1109\/ICASSP.1978.1170394","volume-title":"Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Process, ICASSP \u201978, vol.\u00a03","author":"R.M. Mersereau","year":"1978","unstructured":"Mersereau, R.M., Schafer, R.W.: Comparative study of iterative deconvolution algorithms. In: Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Process, ICASSP \u201978, vol.\u00a03, pp. 192\u2013195. IEEE, Piscataway (1978)"},{"issue":"6","key":"9101_CR21","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1137\/0315061","volume":"15","author":"R. Mifflin","year":"1977","unstructured":"Mifflin, R.: Semismooth and semiconvex functions in constrained optimization. SIAM J. Control Optim. 15(6), 959\u2013972 (1977)","journal-title":"SIAM J. Control Optim."},{"key":"9101_CR22","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. Comm. Pure Appl. Math. 42, 577\u2013685 (1989)","journal-title":"Comm. Pure Appl. Math."},{"key":"9101_CR23","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10107-004-0552-5","volume":"103","author":"Y. Nesterov","year":"2005","unstructured":"Nesterov, Y.: Smooth minimization of non-smooth functions. Math. Program. Ser. A 103, 127\u2013152 (2005)","journal-title":"Math. Program. Ser. A"},{"issue":"3","key":"9101_CR24","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s10851-007-0650-0","volume":"27","author":"M. Ng","year":"2007","unstructured":"Ng, M., Qi, L., Yang, Y., Huang, Y.: On semismooth Newton\u2019s methods for total variation minimization. J. Math. Imaging Vision 27(3), 265\u2013276 (2007)","journal-title":"J. Math. Imaging Vision"},{"key":"9101_CR25","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"L.I. Rudin","year":"1999","unstructured":"Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60, 259\u2013268 (1999)","journal-title":"Phys. D"},{"issue":"4","key":"9101_CR26","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1109\/PROC.1981.11987","volume":"69","author":"R.W. Schafer","year":"1981","unstructured":"Schafer, R.W., Mersereau, R.M., Richards, M.A.: Constrained iterative restoration algorithms. Proc. IEEE 69(4), 432\u2013450 (1981)","journal-title":"Proc. IEEE"},{"key":"9101_CR27","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/BF02592050","volume":"26","author":"G. Strang","year":"1983","unstructured":"Strang, G.: Maximal flow through a domain. Math. Programming 26, 123\u2013143 (1983)","journal-title":"Math. Programming"},{"key":"9101_CR28","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1137\/S1052623494274970","volume":"7","author":"D. Sun","year":"1997","unstructured":"Sun, D., Han, J.: Newton and quasi-Newton methods for a class of nonsmooth equations and related problems. SIAM J. Optim. 7, 463\u2013480 (1997)","journal-title":"SIAM J. Optim."},{"key":"9101_CR29","first-page":"148","volume-title":"Scientific Computing: Proceedings of the Workshop","author":"C.R. Vogel","year":"1997","unstructured":"Vogel, C.R.: Solution of linear systems arising in nonlinear image deblurring. In: Golub, G., Lui, S., Luk, F., Plemmons, R. (eds.) Scientific Computing: Proceedings of the Workshop, pp. 148\u2013158. Springer, Hong Kong (1997)"},{"key":"9101_CR30","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717570","volume-title":"Computational Methods for Inverse Problems","author":"C.R. Vogel","year":"2002","unstructured":"Vogel, C.R.: Computational Methods for Inverse Problems. SIAM, Philadelphia (2002)"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-008-9101-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-008-9101-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-008-9101-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T17:08:11Z","timestamp":1559149691000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-008-9101-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9,24]]},"references-count":30,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2009,10]]}},"alternative-id":["9101"],"URL":"https:\/\/doi.org\/10.1007\/s10444-008-9101-8","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9,24]]}}}