[CVPR 2013] Fast Convolutional Sparse Coding

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1、FastConvolutionalSparseCodingHiltonBristow,1,3AndersEriksson2andSimonLucey31QueenslandUniversityofTechnology,Australia2TheUniversityofAdelaide,Australia3CSIRO,Australia{hilton.bristow,simon.lucey}@csiro.au,anders.eriksson@adelaide.edu.auAbstractSparsecodinghasbecomeanincre

2、asinglypopularmethodinlearningandvisionforavarietyofclassifi-cation,reconstructionandcodingtasks.Thecanonicalapproachintrinsicallyassumesindependencebetweenobservationsduringlearning.Formanynaturalsig-nalshowever,sparsecodingisappliedtosub-elements(i.e.patches)ofthesignal,w

3、heresuchanassumptionisinvalid.Convolutionalsparsecodingexplicitlymod-elslocalinteractionsthroughtheconvolutionoperator,howevertheresultingoptimizationproblemisconsid-erablymorecomplexthantraditionalsparsecoding.Inthispaper,wedrawuponideasfromsignalprocessingandAugmentedLag

4、rangeMethods(ALMs)toproduceafastalgorithmwithgloballyoptimalsubproblemsandsuper-linearconvergence.Figure1.Aselectionoffilterslearnedfromanunalignedsetoflions.ThespatiallyinvariantalgorithmproducesexpressionofgenericGabor-likefiltersaswellasspecialized1.Introductiondomainspec

5、ificfilters,suchasthehighlighted“eye”.Sparsedictionarylearningalgorithmsaimtofactor-izeanensembleofinputvectors{x}Nintoalin-n=1Sparsecodinghasafundamentaldrawbackhowever,earcombinationofovercompletebasiselementsD=asitassumestheensembleofinputvectors{x}Nnn=1[d1,...,dK]undersp

6、arsityconstraints.Oneoftheareindependentofoneanother,i.e.thecomponentsmostpopularformsofthisalgorithmattemptstosolve,ofthebasesarearbitrarilyalignedwithrespecttothestructureofthesignal.XN12Thisindependenceassumption,whenappliedtonat-argmin

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