{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:55Z","timestamp":1787336995036,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>In this paper we formulate a time dependent model to approximate the solution to the nonlinear total variation optimization problem for deblurring and noise removal introduced by Rudin and Osher [ Total variation based image restoration with free local constraints, in Proceedings IEEE Internat. Conf. Imag. Proc., IEEE Press, Piscataway, NJ, (1994), pp. 31--35] and Rudin, Osher, and Fatemi [ Phys. D, 60 (1992), pp. 259--268], respectively. Our model is based on level set motion whose steady state is quickly reached by means of an explicit procedure based on Roe's scheme [ J. Comput. Phys., 43 (1981), pp. 357--372], used in fluid dynamics. We show numerical evidence of the speed of resolution and stability of this simple explicit procedure in some representative 1D and 2D numerical examples.<\/jats:p>","DOI":"10.1137\/s1064827599351751","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"387-405","source":"Crossref","is-referenced-by-count":206,"title":["Explicit Algorithms for a New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal"],"prefix":"10.1137","volume":"22","author":[{"given":"Antonio","family":"Marquina","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stanley","family":"Osher","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375127"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S003614299529230X"},{"key":"R3","unstructured":"P. Blomgren and T. F. Chan,\n                      Modular Solvers for Constrained Image Restoration Problems\n                      , UCLA CAM report 97\u201052, UCLA, Los Angeles, 1997."},{"key":"R4","doi-asserted-by":"crossref","unstructured":"P. Blomgren, T. F. Chan, and P. Mulet,\n                      Extensions to total variation denoising\n                      , Proceedings SPIE 97, San Diego, SPIE, Bellingham, WA, 1997.","DOI":"10.1117\/12.279496"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050258"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596299767"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1109\/34.120331"},{"key":"R8","volume-title":"The theory of Tikhonov regularization for Fredholm equations of the first kind","author":"Groetsch C.","year":"1984"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90031-3"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8629-1"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1978-0501995-4"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/0915054"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759528507X"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/0727053"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90002-2"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(81)90128-5"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/0109044"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"L. Rudin and S. Osher,\n                      Total variation based image restoration with free local constraints\n                      , in Proceedings IEEE Internat. Conf. Imag. Proc., Austin, TX, IEEE Press, Piscataway, NJ, (1994), pp. 31\u201335.","DOI":"10.1109\/ICIP.1994.413269"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90242-F"},{"key":"R20","unstructured":"J. A. Sethian,\n                      Level Set Methods\n                      , Cambridge University Press, London, 1996."},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90222-2"},{"key":"R22","unstructured":"A. N. Tikhonov and V. Y. Arsenin,\n                      Solutions of Ill\u2010Posed Problems\n                      , John Wiley, New York, 1977."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1145\/321150.321157"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1997.5757"},{"key":"R25","unstructured":"L. Vese,\n                      Variational Problems and PDE\u2019s for Image Analysis and Curve Evolution\n                      , Ph.D. thesis, University of Nice, 1996."},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/0917016"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827599351751","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:39:42Z","timestamp":1787333982000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827599351751"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827599351751"],"URL":"https:\/\/doi.org\/10.1137\/s1064827599351751","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}