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1、1EstimationofOptimalPDE-basedDenoisingintheSNRSenseGuyGilboa,NirSochenandYehoshuaY.ZeeviAbstract—ThispaperisconcernedwithfindingthebestPDE-prisingly,wasseriouslyaddressedinthecontextofPDE-basedbaseddenoisingprocess,outofasetofpossibleones.Wefocusei-imageprocessingonlybyafewstudies[11
2、],[18],[24].theronfindingtheproperweightofthefidelitytermintheenergyWederiveanecessaryconditionforoptimalityintheSignal-minimizationformulation,orondeterminingtheoptimalstoppingto-NoiseRatio(SNR)sense.Fromapracticalviewpoint,thetimeofanonlineardiffusionprocess.Anecessaryconditionforac
3、hievingmaximalSNRisstated,conditionsuggestsanumericalmethodthatshouldbefollowedbasedonthecovarianceofthenoiseandtheresidualpart.WeforthepurposeofmaximizingtheSNRofthefilteredimage.providetwopracticalalternativesforestimatingthiscondition,byTwoalgorithmsfortheparametercalculationarepr
4、oposed,observingthatthefilteringoftheimageandthenoisecanbeap-basedontheabovecondition,yieldingfairlyaccurateestimates.proximatedbyadecouplingtechnique,withrespecttotheweightFromatheoreticalviewpoint,thisfacilitatesthecomputationofortimeparameters.Ourautomaticalgorithmobtainsquiteaccu
5、-rateresultsonavarietyofsyntheticandnaturalimages,includingupperandlowerboundsoftheoptimalstrategy.piecewisesmoothandtexturedones.Weassumethatthestatis-Next,wepresentananalysisoftheoptimalparameterfromaticsofthenoisewerepreviouslyestimated.Noa-prioriknowledgeSNRviewpoint.Wealsoexami
6、nethepopulardenoisingstrat-regardingthecharacteristicsofthecleanimageisrequired.egy,basedonMorozov'sdiscrepancyprinciple[13],usedinAtheoreticalanalysisiscarriedout,whereseveralSNRper-thefieldofregularizationtheory.Thismethodwasmostno-formanceboundsareestablishedfortheoptimalstrategya
7、ndforawidelyusedmethod,whereinthevarianceoftheresidualparttablyusedinvariationalimageprocessingintheseminalRudin-equalsthevarianceofthenoise.Osher-Fatemipaper[18].Theselectionoftheweightofthefi-delitytermissuchthatthevarianceoftheresidualpartequalsthatofthenoise.AlowerboundontheSNRpe
8、rformanceofI.INTROD
