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1、AppliedMathematicsandComputation217(2011)5392–5403ContentslistsavailableatScienceDirectAppliedMathematicsandComputationjournalhomepage:www.elsevier.com/locate/amcqSplitBregmanmethodforthemodifiedlotmodelinimagedenoisingab,⇑abYu-FeiYang,Zhi-FengPang,Bao
2、-LiShi,Zhi-GuoWangaCollegeofMathematicsandEconometrics,HunanUniversity,Changsha410082,ChinabCollegeofMathematicsandInformationScience,HenanUniversity,Kaifeng475000,ChinaarticleinfoabstractKeywords:InthispaperasplitBregmaniterationisproposedforthemodifi
3、edLOTmodelinimageImagerestorationdenoising.WefirstusethesplitBregmanmethodtosolvetheROFmodelwhichcanbeROFmodelseenasanapproximateformofthefirststepoftheoriginalLOTmodel.ThenweuseaLLTmodelmodifiedsplitBregmanmethodtofitthesecondstepoftheLOTmodelandgivethec
4、on-LOTmodelvergenceoftheproposedsplitBregmanmethod.SeveralnumericalexamplesarearrangedSplitBregmanmethodtoshowtheeffectivenessoftheproposedmethod.Ó2010ElsevierInc.Allrightsreserved.1.IntroductionImagedenoisingisoneofmostimportantinverseproblemsinimage
5、processingandcomputervision.Theobjectiveistofindtheunknowntrueimageufromanobservedimagefdefinedbyf¼uþg;ð1:1Þwheregisanoisewiththestandardderivationr.However,thechallengingaspectofthisproblemistodesignmethodswhichcaselectivelysmoothanoisyimagewithoutlosi
6、ngsignificantfeaturessuchasedgesandtextures.Forpreservingimageedges,someapproachesarebasedonthestatisticsmethodsuchasthenonparametricestimationofadiscontinuoussurface[19,26,27]andwaveletmethod[7,8].AnotherapproachesarebasedontheTikhonovregularizationme
7、thodinthesenseofPDE[7,25]suchasthemostsuccessfulandpopulartechniquesisthetotalvariationmodel,whichwasfirstproposedbyRudin,OsherandFatemi(calledtheROFmodel)[29]asfollows:Zk2minE1ðuÞ¼kufkL2ðXÞþjDujdx;ð1:2Þu2BVðXÞ2Xwherek>0istheregularizationparameter,Xi
8、saboundeddomainwithLipschitzboundaryandBV(X)isdefinedbyZ1BVðXÞ¼u2LðXÞ:jDujdx<1;XwhereZZ12jDujdx¼supudivuðxÞdx:uðxÞ2CðX;RÞ;juðxÞj61;ð1:3Þ0XXqTheworkissupportedbytheNNSFofChina(Nos.60872129and60835004)andtheScienceandTechnologyProjectofHunanP
