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1、FastGradient-BasedAlgorithmsforConstrainedTotalVariationImageDenoisingandDeblurringProblemsAmirBeckyandMarcTeboullezMay29,2009AbstractThispaperstudiesgradient-basedschemesforimagedenoisinganddeblurringprob-lemsbasedonthediscretizedtotalvariation(TV)minimizationmodelwith
2、con-straints.WederiveafastalgorithmfortheconstrainedTV-basedimagedeburringproblem.Toachievethistaskwecombineanaccelerationofthewellknowndualapproachtothedenoisingproblemwithanovelmonotoneversionofafastiterativeshrinkage/thresholdingalgorithm(FISTA)wehaverecentlyintroduce
3、d.Theresult-inggradient-basedalgorithmsharesaremarkablesimplicitytogetherwithaprovenglobalrateofconvergencewhichissigni cantlybetterthancurrentlyknowngradientprojections-basedmethods.OurresultsareapplicabletoboththeanisotropicandisotropicdiscretizedTVfunctionals.Initialn
4、umericalresultsdemonstratetheviabil-ityandeciencyoftheproposedalgorithmsonimagedeblurringproblemswithboxconstraints.1IntroductionInthispaperweproposefastgradient-basedalgorithmsfortheconstrainedtotalvariation(TV)basedimagedenoisinganddeblurringproblems.Thetotalvariation
5、modelhasbeenintroducedbyRudin-OsherandFatemi(ROF)in[24]asaregularizationapproachcapableofhandlingproperlyedgesandremovingnoiseinagivenimage.Thismodelhasproventobesuccessfulinawiderangeofapplicationsinimageprocessing.ThediscretepenalizedversionoftheTV-baseddeburringmodelc
6、onsistsofsolvinganunconstrainedconvexminimizationproblemoftheform,2minkA(x) bk+2kxkTV;(1.1)xwherekkisanorminsomegivenvectorspace,bistheobservednoisydata,Aisalinearmaprepresentingsomeblurringoperator,kkTVisadiscreteTV(semi)-norm,andxisThisresearchispartiallysupportedb
7、ytheIsraelScienceFoundation,ISFgrant#489-06.yDepartmentofIndustrialEngineeringandManagement,Technion
8、IsraelInstituteofTechnology,Haifa32000,Israel.E-mail:becka@ie.technion.ac.ilzSchoolofMathematicalSciences,Tel-AvivUniversity,Ramat-Aviv69978,Israel,E-mail:teboulle@math.t
9、au.ac.il1thedesiredunknownimagetoberecovered(seeSection2formoreprecisedetails).Theregularizationparamet
