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1、INVITEDPAPEROntheRoleofSparseandRedundantRepresentationsinImageProcessingInimageprocessing,fillinginmissingportionsofimagesorclearingupblurredimagescanberapid,efficient,accurate,andrelativelysimpleprocedures.ByMichaelElad,SeniorMemberIEEE,Ma´rioA.T.Figueiredo,FellowIEE
2、E,andYiMa,SeniorMemberIEEEABSTRACT
3、MuchoftheprogressmadeinimageprocessinginI.INTRODUCTIONthepastdecadescanbeattributedtobettermodelingofimageAcloseinspectionoftheprogressmadeinthefieldofcontentandawisedeploymentofthesemodelsinrelevantimageprocessinginthepastseveraldeca
4、desrevealsthatapplications.Thispathofmodelsspansfromthesimple‘2-normmuchofitisadirectconsequenceofthebetterimagesmoothnessthroughrobust,thusedgepreserving,measuresofmodelingemployed.Armedwithastrongerandmoresmoothness(e.g.totalvariation),anduntiltheveryrecentreliablemo
5、del,onecanbetterhandleapplicationsrangingmodelsthatemploysparseandredundantrepresentations.Infromsampling,denoising,restoration,andreconstructionthispaper,wereviewtheroleofthisrecentmodelinimageininverseproblemsallthewaytocompression,detection,processing,itsrationale,a
6、ndmodelsrelatedtoit.Asitturnsout,separation,andbeyond.Indeed,theevolutionofmodelsthefieldofimageprocessingisoneofthemainbeneficiariesforvisualdataisattheheartoftheimage-processingfromtherecentprogressmadeinthetheoryandpracticeofliterature.sparseandredundantrepresentati
7、ons.WediscusswaystoWhatisamodelandwhydoweneedone?Weprovideemploythesetoolsforvariousimage-processingtasksandaninitialanswertothesequestionsthroughasimplepresentseveralapplicationsinwhichstate-of-the-artresultsexampleofnoiseremovalfromanimage.Givenanoisyareobtained.imag
8、e,adenoisingalgorithmisessentiallyrequiredtoseparatethenoiseformthe(unknown)cleanimage.SuchKEYWORDS
9、Deconvolution;denoising;dictionarylearning;aseparationclearlyrequiresaclosefamiliaritywiththeframes;inpainting;redundantdictionaries;sparserepresenta-characteristicsofbo
10、ththenoiseandtheoriginalimage.tions;superresolution;waveletsKnowingthatthenoiseisadditive,white,andGaussian(AWG)isago