On the Role of Sparse and Redundant Representations in Image Processing

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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