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1、886IEEETRANSACTIONSONSIGNALPROCESSING,VOL.46,NO.4,APRIL1998Wavelet-BasedStatisticalSignalProcessingUsingHiddenMarkovModelsMatthewS.Crouse,StudentMember,IEEE,RobertD.Nowak,Member,IEEE,andRichardG.Baraniuk,SeniorMember,IEEEAbstractÐWavelet-basedstatisticalsignalproc
2、essingoftenencounteredinpractice.Thesenewmodelsleadtoso-techniquessuchasdenoisinganddetectiontypicallymodelthephisticatedprocessingtechniquesthatcoordinatethenonlinearwaveletcoefficientsasindependentorjointlyGaussian.Theseprocessingamongstcoefficientstooutperformcur
3、rentwavelet-modelsareunrealisticformanyreal-worldsignals.Inthispaper,basedalgorithms.Themodelsaredesignedwiththeintrinsicwedevelopanewframeworkforstatisticalsignalprocessingbasedonwavelet-domainhiddenMarkovmodels(HMM's)thatpropertiesofthewavelettransforminmind.con
4、ciselymodelsthestatisticaldependenciesandnon-Gaussianstatisticsencounteredinreal-worldsignals.Wavelet-domainHMM'saredesignedwiththeintrinsicpropertiesoftheA.TheDiscreteWaveletTransformwavelettransforminmindandprovidepowerful,yettractable,Thewavelettransformisanato
5、micdecompositionthatprobabilisticsignalmodels.EfficientexpectationmaximizationalgorithmsaredevelopedforfittingtheHMM'stoobservationalrepresentsaone-dimensional(1-D)signalintermsofsignaldata.Thenewframeworkissuitableforawiderangeofshiftedanddilatedversionsofaprototyp
6、ebandpasswaveletapplications,includingsignalestimation,detection,classification,function,andshiftedversionsofalowpassscalingprediction,andevensynthesis.Todemonstratetheutilityoffunction[8],[9].Forspecialchoicesofthewaveletandwavelet-domainHMM's,wedevelopnovelalgori
7、thmsforsignaldenoising,classification,anddetection.scalingfunctions,theatomsIndexTermsÐHiddenMarkovmodel,probabilisticgraph,wavelets.(1)I.INTRODUCTIONformanorthonormalbasis,andwehavethesignalrepresen-tation[8],[9]HEWAVELETtransformhasemergedasanexcitingTnewtoolfors
8、tatisticalsignalandimageprocessing.Thewaveletdomainprovidesanaturalsettingformany(2)applicationsinvolvingreal-worldsignals,includingestimation[1]±[3],de
