稀疏表示ppt-Michael_Elad

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1、MMSEEstimationforSparseRepresentationModelingMichaelEladTheComputerScienceDepartmentTheTechnion–IsraelInstituteoftechnologyHaifa32000,Israel*JointworkwithIradYavneh&MatanProtterTheCSDepartment,TheTechnionApril6th,2009MMSEEstimationforSparseRepresentationModelingBy:MichaelElad2NoiseRemoval?Inthista

2、lkwefocusonsignal/imagedenoising…Important:(i)Practicalapplication;(ii)Aconvenientplatformfortestingbasicideasinsignal/imageprocessing.ManyConsideredDirections:Partialdifferentialequations,Statisticalestimators,Adaptivefilters,Inverseproblems®ularization,Wavelets,Example-basedtechniques,Sparser

3、epresentations,…MainMassageToday:Severalsparserepresentationscanbefoundandusedforbetterdenoisingperformance–weintroduce,motivate,discuss,demonstrate,andexplainthisnewidea.RemoveAdditiveNoise?MMSEEstimationforSparseRepresentationModelingBy:MichaelElad3BackgroundonDenoisingwithSparseRepresentationsU

4、singMorethanOneRepresentation:IntuitionUsingMorethanOneRepresentation:TheoryACloserLookAttheUnitaryCaseSummaryandConclusionsAgendaMMSEEstimationforSparseRepresentationModelingBy:MichaelElad4PartIBackgroundonDenoisingwithSparseRepresentationsMMSEEstimationforSparseRepresentationModelingBy:MichaelEl

5、ad5RelationtomeasurementsDenoisingByEnergyMinimizationThomasBayes1702-1761Priororregularizationy:Givenmeasurementsx:UnknowntoberecoveredManyoftheproposedsignaldenoisingalgorithmsarerelatedtotheminimizationofanenergyfunctionoftheformThisisin-factaBayesianpointofview,adoptingtheMaximum-A-posterioriP

6、robability(MAP)estimation.Clearly,thewisdominsuchanapproachiswithinthechoiceoftheprior–modelingthesignalsofinterest.MMSEEstimationforSparseRepresentationModelingBy:MichaelElad6SparseRepresentationModelingMKNAfixedDictionaryEverycolumninD(dictionary)isaprototypesignal(atom).Thevectorisgeneratedra

7、ndomlywithfew(sayLfornow)non-zerosatrandomlocationsandwithrandomvalues.Asparse&randomvectorNMMSEEstimationforSparseRepresentationModelingBy:MichaelElad7D-y=-BacktoOurMAPEnergyFunctionTheL0“norm”iseffectivelycoun