{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T02:36:05Z","timestamp":1787711765640,"version":"build-2784847793"},"reference-count":15,"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>The total variation (TV) denoising method is a PDE-based technique that preserves edges well but has the sometimes undesirable staircase effect, namely, the transformation of smooth regions ( ramps) into piecewise constant regions ( stairs). In this paper we present an improved model, constructed by adding a nonlinear fourth order diffusive term to the Euler--Lagrange equations of the variational TV model. Our technique substantially reduces the staircase effect, while preserving sharp jump discontinuities (edges). We show numerical evidence of the power of resolution of this novel model with respect to the TV model in some 1D and 2D numerical examples.<\/jats:p>","DOI":"10.1137\/s1064827598344169","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"503-516","source":"Crossref","is-referenced-by-count":651,"title":["High-Order Total Variation-Based Image Restoration"],"prefix":"10.1137","volume":"22","author":[{"given":"Tony","family":"Chan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antonio","family":"Marquina","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pep","family":"Mulet","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":"10.1088\/0266-5611\/10\/6\/003"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S003614299529230X"},{"key":"R3","unstructured":"P. Blomgren and T. Chan,\n                      Modular Solvers for Constrained Image Restoration Problems\n                      , CAM report 97\u201052, Math Department, University of California at Los Angeles, Los Angeles, CA, November 1997."},{"key":"R4","doi-asserted-by":"crossref","unstructured":"P. Blomgren, T. F. Chan, and P. Mulet,\n                      Extensions to total variation denoising\n                      , in Proceedings Society of Photo\u2010Optical Instrumentation Engineers (SPIE) 97, San Diego, 1997.","DOI":"10.1117\/12.279496"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0729012"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050258"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596299767"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997327075"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1109\/34.120331"},{"key":"R10","unstructured":"C. W. Groetsch,\n                      The Theory of Tikhonov Regularization for Fredholm Integral Equations of the First Kind\n                      , Pitman, Boston, 1984."},{"key":"R11","volume-title":"Time dependent problems and difference methods","author":"Gustafsson Bertil","year":"1995"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90242-F"},{"key":"R13","unstructured":"A. N. Tikhonov and V. Y. Arsenin,\n                      Solutions of Ill\u2010Posed Problems\n                      , John Wiley, New York, 1977."},{"key":"R14","unstructured":"L. Vese,\n                      Variational Problems and PDE\u2019s for Image Analysis and Curve Evolution\n                      , Ph.D. thesis, University of Nice, France, 1996."},{"key":"R15","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\/S1064827598344169","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:39:50Z","timestamp":1787333990000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827598344169"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827598344169"],"URL":"https:\/\/doi.org\/10.1137\/s1064827598344169","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}