A versatile wavelet domain noise filtration techni

SUBMITTEDFORPUBLICATIONTO:IEEETRANS.ONMEDICALIMAGING,JUNE28,20021AVersatileWaveletDomainNoiseFiltrationTechniqueforMedicalImagingAleksandraPizurica,WilfriedPhilips,IgnaceLemahieu,andMarcAcheroyAbstractInthispaper,weproposearobustwaveletdomainmethodfornoisefilteringinmedicalimages.Theproposedmethodadaptsitselftovarioustypesofimagenoiseaswellastothepreferenceofthemedicalexpert:asingleparametercanbeusedtobalancethepreservationof(expert-dependent)relevantdetailsagainstthedegreeofnoisereduction.Thealgorithmexploitsgenerallyvalidknowledgeaboutthecorrelationofsignificantimagefeaturesacrosstheresolutionscalestoperformapreliminarycoefficientclassification.Thispreliminarycoefficientclassificationisusedtoempiricallyestimatethestatisticaldistributionsofthecoefficientsthatrepresentusefulimagefeaturesontheonehandandmainlynoiseontheother.Theadaptationtothespatialcontextintheimageisachievedbyusingawaveletdomainindicatorofthelocalspatialactivity.Theproposedmethodisoflow-complexity,bothinitsimplementationandexecutiontime.Theresultsdemonstrateitsusefulnessfornoisesuppressioninmedicalultrasoundandmagneticresonanceimaging.Intheseapplications,theproposedmethodclearlyoutperformssingle-resolutionspatiallyadaptivealgorithms,intermsofquantitativeperformancemeasuresaswellasintermsofvisualqualityoftheimages.I.IntroductionInmedicalimages,noisesuppressionisaparticularlydelicateanddifficulttask.Atradeoffbetweennoisereductionandthepreservationofactualimagefeatureshastobemadeinawaythatenhancesthediagnosticallyrelevantimagecontent.Imageprocessingspecialistsusuallylackthebiomedicalexpertisetojudgethediagnosticrelevanceofthedenoisingresults.Forexample,inA.Pizurica∗andW.PhilipsarewiththeDepartmentforTelecommunicationsandInformationProcessing(TELIN),GhentUniversity,Sint-Pietersnieuwstraat41,B-9000Gent,Belgium.E-mail:[e-mail],[e-mail],Tel:[phone],Fax:[phone]I.LemahieuiswiththeDepartmentforElectronicsandInformationSystems(ELIS/MEDISIP),GhentUniversity,Sint-Pietersnieuwstraat41,B-9000Gent,Belgium.E-mail:[e-mail],Fax:[phone],Tel:[phone]M.AcheroyiswiththeRoyalMilitaryAcademy,Av.delaRenaissance30,B-1000Brussels,Belgium.E-mail:[e-mail],Fax:[phone],Tel.:[phone]ultrasoundimages,specklenoisemaycontaininformationusefultomedicalexperts[39];theuseofspeckledtextureforadiagnosiswasdiscussedin[18],[35].Also,biomedicalimagesshowextremevariabilityanditisnecessarytooperateonacasebycasebasis[36].Thismotivatestheconstructionofrobustandversatiledenoisingmethodsthatareapplicabletovariouscircumstances,ratherthanbeingoptimalunderveryspecificconditions.Thenotionofrobustnessinmultiscaledenoisingwasaddressedin[19].Inthispaper,weproposeonerobustmethodthatadaptsitselftovarioustypesofimagenoiseaswellastothepreferenceofthemedicalexpert:asingleparametercanbeusedtobalancethepreservationof(expert-dependent)relevantdetailsagainstthedegreeofnoisereduction.Inimagedenoisingoneoftenfacesuncertaintyaboutthepresenceofagiven“featureofinterest”(e.g.,animageedge)inanoisyobservation.Duetothesparsityofthewaveletrepresentation,theMiddleton’soptimumcoupleddetectionandestimationapproach[28]seemswellsuitedforwaveletdomainimagedenoising.Totheauthors’knowledgesuchapproacheshavereceivedlittleattentionsofarinwaveletdomainfiltering.Bayesianmethods[2],[5],[37]taketheuncertaintyofthesignalpresenceintoaccountimplicitly,assumingaBernoulliprocessonthewaveletcoefficients[20]andusingGaussianmixturemodelsfortheprobabilitydensityfunctionsofthewaveletcoefficients.Re-latedhereto,butmoresophisticated,spatiallyadaptivemethodsusuallyemploycomplexalgorithms,basedonhiddenMarkovtreemodels[6],[10]orMarkovrandomfieldpriormodels[17],[23],[31].Otherrecenttrendsinwavelet-basedimagedenoisingincludeapplyingdifferenttypesoffilteringinsupposedlysmoothandsupposedlyheterogeneousor“edged”imageregions[12],[21],spatiallyadaptivethresholding[4]andlocallyadaptiveWienerfiltering[29].Recently,weproposedanalternative,low-complexityjointdetectionandestimationmethod[32].Inparticular,themethodappliestheminimummeansquarederrorcriterionassumingthateachwaveletcoefficientrepresentsa“signalofinterest”withaprobabilityp1,leadingtothegeneralizedlikelihoodratio[28]formulationinthewaveletdomain.In[32],weintroducedananalyticalmodelfortheprobabilityofsignalpresence,whichisadaptedtotheglobalcoefficienthistogramandtoalocalindicatorofspatialactivity(e.g.,thelocallyaveragedmagnitudeofthewaveletcoefficients).Inthispaper,weproposearelated,butmoreflexiblemethod,whichisapplicabletovariousandunknowntypesofimagenoise.Inparticular,wedonotrelyontheexactpriorknowledgeofthenoise3distribution,whichallowsonetoestimatetheprobabilitydensityfunction(pdf)ofnoise-freewaveletcoefficientsfromthenoisyhistogram.Instead,weemployapreliminarydetectionofthewaveletcoefficientsthatrepresentthefeaturesofinterestinordertoempiricallyestimatetheconditionalpdf’softhecoefficientsgiventheusefulfeaturesandgivenbackgroundnoise.Atthesametime,thepreliminarycoefficientclassificationisalsoexploitedtoempiricallyestimatethecorres