Introduction-to-sparse-representation.ppt

IntroductiontoSparseRepresentationandSomeApplicationsonTextureClassification,XieJin,Outline,SparserepresentationofsignalsTextureclassificationviasparsetextonlearningTextonencodinginducedstatisticalfeaturesfortextureclassificationOpenproblems,Sparserepresentationofsignals,Signalprocessingtools:FT(Fouriertransform)STFT(ShorttimeFouriertransform)Wavelettransform-Optimalfor1Dsignal-Notoptimalfor2Dsignal(images):notadaptivetothecontentintheimageCurevelet,countourletandbandlettransform:Constructbettertransformbasestorepresentimages,Sparserepresentationofsignals,Sparserepresentationofsignals,Sparserepresentationofsignals,Sparserepresentationofsignals,Sparserepresentationofsignals,Sparserepresentationofsignals,SolvingL0optimizationisanNP-hardproblem.Greedymethods:MatchingPursuit,OrthogonalMatchingPursuit(Mallat93).Relaxationmethods:Insomecases,solvingL0optimizationcanbeequaltosolveL1optimization(Candes,TerrenceTao,Donoho,2004):Algorithms:l1magic,l1-ls,homotopyandaugmentedLagrangianmethodAllanyangetal:AReviewofFast11-MinimizationAlgorithmsforRobustFaceRecognition(SIAM,Review),Compressivesensing,Textureclassificationwithdictionarylearning,Textureclassificationwithdictionarylearning,Textureclassificationwithdictionarylearning,Textureclassificationwithdictionarylearning,Textureclassificationviasparsetextonlearning,Motivation,Textureclassificationviasparsetextonlearning,TheK-meansclusteringalgorithmisbasedonthel2-normEuclideandistancesothattheelementsofaclusterwillhaveaball-likedistribution.ThelearnedKball-likeclusters,nonetheless,maynotbeabletocharacterizereasonablywelltheintrinsicfeaturespaceofthetextureimages.TheK-meansclusteringmethodcanbeviewedasaspecialcaseoftheSparseCoding(SC).SCcanachieveamuchlowerreconstructionerrorduetothelessrestrictiveconstraint.,Textureclassificationviasparsetextonlearning,Idea:Wecanusethesparsecodingtoreplacek-meanstolearnatexturedictionary.Andextracttexturefeaturesfromthelearneddictionary.Pre-processingsteps:Alltextureimagesareconvertedtogreylevelimagesandarenormalizedtohavezeromeanandunitstandarddeviation.Asquareneighborhoodaroundeachpixelintheimageistakenandavectorisformedalongtherow.PatchvectorsarecontrastnormalizedusingtheWeberslaw.,Textureclassificationviasparsetextonlearning,Textureclassificationviasparsetextonlearning,Usetextonstorepresenttexture:,Textureclassificationviasparsetextonlearning,Textureclassificationviasparsetextonlearning,ExperimentalresultsontheCUReTtexturedatabaseTheCUReTtexturedatabasecontains61classes,eachconsistingof92images.Ithasbothlargeinter-classconfusionandintra-classvariation.Theimagesofaclassareobtainedundertheunknownviewpointandilluminationchanges,andsomedifferentclasseslooksimilarinappearance.Figure(a)and(b)showtwodifferentkindsoftextureswhiletheimagesappearsimilar.,Textureclassificationviasparsetextonlearning,Textureclassificationviasparsetextonlearning,Textureclassificationviasparsetextonlearning,Multi-scaleestimationusingdictionarylearningCurrentdictionarylearningmethodslackthemulti-scaleproperty.Boazophir,MichaelLustingandMichaelElad.Multi-scaledictionarylearningusingwavelet.IEEET