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1、INVITEDPAPERDictionariesforSparseRepresentationModelingDigitalsamplingcandisplaysignals,anditshouldbepossibletoexposealargepartofthedesiredsignalinformationwithonlyalimitedsignalsample.ByRonRubinstein,StudentMemberIEEE,AlfredM.Bruckstein,MemberIEEE,andMichaelElad,SeniorMemberIEEEABSTRAC
2、T
3、Sparseandredundantrepresentationmodelingoftime.Thisrepresentation,whileconvenientforthepur-dataassumesanabilitytodescribesignalsaslinearcombina-posesofdisplayorplayback,ismostlyinefficientforanal-tionsofafewatomsfromapre-specifieddictionary.Assuch,ysistasks.Signalprocessingtechniquesc
4、ommonlyrequirethechoiceofthedictionarythatsparsifiesthesignalsiscrucialmoremeaningfulrepresentationswhichcapturetheusefulforthesuccessofthismodel.Ingeneral,thechoiceofapropercharacteristicsofthesignalVforrecognition,therepre-dictionarycanbedoneusingoneoftwoways:i)buildingasentationshoul
5、dhighlightsalientfeatures;fordenoising,sparsifyingdictionarybasedonamathematicalmodelofthetherepresentationshouldefficientlyseparatesignalanddata,orii)learningadictionarytoperformbestonatrainingnoise;andforcompression,therepresentationshouldset.Inthispaperwedescribetheevolutionofthesetw
6、ocapturealargepartofthesignalwithonlyafewcoeffi-paradigms.Asmanifestationsofthefirstapproach,wecovercients.Interestingly,inmanycasestheseseeminglydiffer-topicssuchaswavelets,waveletpackets,contourlets,andentgoalsalign,sharingacoredesireforsimplification.curvelets,allaimingtoexploit1-Dan
7、d2-DmathematicalmodelsRepresentingasignalinvolvesthechoiceofadictionary,forconstructingeffectivedictionariesforsignalsandimages.whichisthesetofelementarysignalsVoratomsVusedtoDictionarylearningtakesadifferentroute,attachingthedecomposethesignal.Whenthedictionaryformsabasis,dictionarytoa
8、setofexamplesitissupposedtoserve.Fromeverysignalisuniquelyrepresentedasthelinearcombi-theseminalworkofFieldandOlshausen,throughtheMOD,thenationofthedictionaryatoms.InthesimplestcasetheK-SVD,theGeneralizedPCAandothers,thispapersurveysthedictionaryisorthogonal,andtherepresentatio
