Projection space denoising with bilateral filtering and CT

ProjectionspacedenoisingwithbilateralfilteringandCTnoisemodelingfordosereductioninCTArmandoManducaa͒DepartmentofPhysiologyandBiomedicalEngineering,MayoClinicCollegeofMedicine,Rochester,Minnesota55905andDepartmentofRadiology,MayoClinicCollegeofMedicine,Rochester,Minnesota55905LifengYuDepartmentofRadiology,MayoClinicCollegeofMedicine,Rochester,oandNataliaKhaylovaDepartmentofPhysiologyandBiomedicalEngineering,MayoClinicCollegeofMedicine,Rochester,fler,ough,erDepartmentofRadiology,MayoClinicCollegeofMedicine,Rochester,Minnesota55905͑Received15May2009;revised8August2009;acceptedforpublication29August2009;published2October2009͒Purpose:Toinvestigateanovellos:Thedenoisingalgorithmisbasedonbilateralfiltering,whichsmoothsvaluesusingaweightedaverageinalocalneighborhood,withweightsdeterminedaccordingtobothspatialproximityandfilteringislocallyadaptiveandcanpreserveimportantedgeinformationinthesinogram,semodelthattakesintoaccountthebowtiefilterandpatient-specificautomatichorsevaluatedthenoise-resolutionpropertiesofbilateralfilteringincorporatingsuchaCTnoisemodelinphantomstudiesans:Onathinwirephantom,thenoise-resolutionpropertiesweresignificantlyimprovedwitse-resolutionprop-ertiesonlow-dose͑40mAs͒dataafterdenoisingappatecontrastplatephantomshowedimproveddepictionoflow-contrastplateswiththedenoisingalgrimprovementinnoise-resolutionpropertieswasfoundonCTcolonog-raphydataandonfiveabdominallow-energy͑80kV͒abdominalcase,aboard-certifiedsubspecializedradiologistratedthedenoised80kVimagesmarkedlysuperiorinimagequalitycomparedtothecommerciallyavailablereconstructions,anddenoisingimprovedtheimagequalitytotheposions:TheresultsdemonstratethatbilateralfilteringincorporatingaCTnoisemodelcanachieveasignificantlybetternoise-provementinnoise-resolutionpropertiescanbeusedforimprovingimagequalityinCTandcanbetranslatedintosubstantialdosereduction.©2009AmericanAssociationofPhysicistsinMedicine.͓DOI:10.1118/1.3232004͔Keywords:CT,radiationdose,noisereduction,bilateralfiltering,UCTIONRadiationexposureandtheassociatedriskofcancerforpa-tientsreceivingCTexaminationshavebeenanincreasingconcerninrecentyears.1,2Itiscr,dosereductiongenerallyleadstoanincreasedlevelofnoiseinthemeasuredprojectiondataandthesubsequentreconstructedimages,.36„11…,November2009ManytechniqueshavebeendevelopedforcontrollingnoiseinCT,operatingoneithertherawprojectionmeasure-ment,thelog-transformedsinogram,duringimagerecon-struction,oronimagesafterreconstruction.3–10Inconven-tionalshift-invariantfiltrationappliedduringimagereconstruction,thesuppressionofthehigh-frequencycom-ponentinthesinogramisperformedwithasimpleassump-tionthatallthemeasurementsareequallyreliable,whichmayresultinseveredegradationofspatialresolution.3–8Moresophisticatedmethodshavebeendevelopedtoadap-©.49110094-2405/2009/36„11…/4911/9/$25.00

4912Manducaetal.:ProjectionspacedenoisingwithbilateralfilteringinCT4912tivelysmootsedanadaptivetrimmedmeanfiltertosmooththedatawiththefiilarexceptthatitwasgeneralizedtoincludeboththe2Ddetectorarrayandtheangulardimensionandusedadirthesemethodsarecurrentlyimplementedonclinicalscannersmaiherapproacheshavealsobeenproposedtoincorporatemoreexplicitstatisticalmodelsandtoiterativelyrestorethelog-transformeddatabyoptimizingapenalizedweightedleast-squaresorlikelihoodobjectivefunction,insomecasesbyrelatingthesinogramvaluetoitsvariance,thusempiri-callycharacterizingthenoiseofthesinogramvalueafterprocessing͑beam-hardeningcorrection,calibration,etc.͒.6,7OtherapproachesmodelCTnoiseinamorecompleteway,including8,9compoundPoisson,off-focal,cross-talk,ivereconstructionmethodscanachievesig-nificantdenoisingbutattheexpenseofverylongcomputa-tiontimes.10Techniquesbasedentirelyonimagespacehavealsobeendescribed,takingadvantageoftheimagestructuretosmoothnoisewhilepreservingedgesbutsufferingfromthe11complicated–work,thodisbasedonbilateralfiltering,14whichsmoothsthesinogrambyusingaweightedaverageinalocalneighborhood,withtheweightsdeter-minedaccordingtoboththespatialproximityandifilteringislocallyadaptiveandcanpreserveimpor-tantedgeinformationinthesinogram,rmore,sinceitorigi-natedfromthestatisticalframeworkofmaximumaposte-riori͑MAP͒estimation,16aCTnoisemodelcanbeincorpo-rated,atDemirkaya17proposedanisotropicdiffusionfilteringinprojectionspace,butwithacrudenoisemodelandonlyshowingresultsonasyntheticallycorruptedShepp–omedenoisingorsinogramrestorationmethodshavebeendevelopedtosmooththeprojectiondatabytakingexplicitstatisticalmodelsintoaccount,6–9theedtoadaptivefiltersdevelopedtosuppressthestreakingartifactscausedbythephotonstarvationalongsomedirections,4,5theproposedapproachaimstoperformnoisered,weintro-ducebilateralfilteringanditsapplicationtoCTdatadenois-ing,describetheeffectsofthebowtiefilterandautomaticexposurecontrolandtheirinclusionintheCTnoisemodel,MedicalPhysics,Vol.36,No.11,,y,ralfilteringBilateralfilteringwasoriginallyproposedbyTomasiandManduchiasanoniterativeandlocallyadaptivemethodforremovingadditivenoisefromimageswhilepreservingedgeinformation.14Inadditiontoitsintuitiveappeal,the16bilateralfieQisastationaryGaussianprocesswithameanofQQ=Q+x,͑1͒boldletterandthecorrespondingnormallettertodenoteastochasticprocessanditsmean,oretheoriginalimageQfromthenoisecon-taminatedimageQ,weconsiderminimizingtheenergyfunc-tionalE͑Q͒=͚P1͑i,j͒P2͑i,j͒͑2͒i෈Ij͚,෈⍀iwhereP1calculatesaweightaccordingtothespatialdis-tancebetweenthecenterpixelandaneighboringpixelandthesecondpenaltyfactorPdifference2calculatesaweightaconally,jistheindexofaneighbor-hoodpixelinsidearegionof⍀icenteredonpixeli,zingthisfunctionalencourageslocalgroupsofpixelstobeofsimilarintensity,er,intherestrictedcasewhereonlyimmediateneighborsareinvestigatedandthespatialpenaltyfunctionP1istakenastheidentityoperator,Eq.͑1͒isthesamefunctionalthatisminimizedbytheclassicalaniso-tropicdiffusionprocessforimagedenoising.15Whiletherearemanypossibilitiesforchoosingthepen-altyfunctionsP1andP2,themostcommonassignmentsaretheGaussianpenaltiesgivenbyPͩ͑i−j͒21͑i,j͒=exp−2d2ͪ,͑3͒P=1−expͩ−͑Qi−Qj͒22͑i,j͒2␴2ͪ,͑4͒whereparametersdand␴caningElad,thebilateralfilterarisesasthefirstiterationofaJacobiprocessminimizingEq.͑2͒andisformallydefinedbytheweightedaveragingofagivenimagepixelQi,namely,

4913Manducaetal.:ProjectionspacedenoisingwithbilateralfilteringinCT4913Qˆ͚j෈⍀iW1͑i,j͒W2͑i,j͒Qji=͚j෈⍀iW1͑i,j͒W2͑i,j͒,͑5͒whereW1andWcancel,2arethedifferentialsofP1andP2and,aftercertainfactorsWͩ͑i−j͒21͑i,j͒=P1͑i,j͒=exp−2d2ͪ,W,j͒=expͩ−͑Qi−Qj͒22͑i2␴2ͪ,͑6͒hespecificationinEqs.͑3͒and͑4͒withGaussianweightingfunctions,thebilateralfilterisidenticaltotheNadaraya–e-peatediterationsarepossibletofurtherminimizetheenergyfunctional͑2͒,inpractice,onlyasinglepassofthebilateralfirmore,aseparableapproximationofthebilateralfilter,asproposedbyPhamandvanVliet,18isavailableandallowsforadramaticincreaseincomputationalperformancewithlittletonodegradationineffiproximationconsistssimplyofrunningaone-dimensionalfilterinonedirectionfirst,thenapplyingthefiltertotheresultsofthisstepintheotherdirection,applicationsinthiswork,emodelDenoisingwithbilateralfilteringcanbedirectlyappliedinimagespaceafterreconstruction,andindeedthesharperedgestherearewellsuitedtotechniqueslikebilateralfilter-ing,butthenoisemodelinimagesp-trast,noiseinprojectionspaceisrelativelyeasiertomodelundercertainsimplifistudy,wewillfocusonlyontheapplicationofbilateralfinCTimagesoriginatesfromdatanoiseinthepro-jectionmeasurement,whichhastwoprincipalsources:ctronicnoiseistheresultofelectronicflghacurrentCTdetectorisnotaphoton-countingel-ementbutanenergyintegratorthatgeneratesasignalpro-portionaltothetotalenergydepositedinthedetector,aphoton-countingmodelisstillagoodapproximationandiswidely,19used,20forcharacterizingnoisepropertiesoftheCTdata.10Moreaccuratenoisemodelshavebeeninvesti-gated,suchasthecompoundPoissonmodelthattakesintoaccountthepolychromaticx-raybeamandenergyintegration.21Asexplainedtherein,theactualresidualerrorintroducedbyaphoton-countingmodelisonlyafewpercentfortypicalphotonflindicatedinthatwork,theimpactfromthebowtiefilterandMedicalPhysics,Vol.36,No.11,ofx-raybeambowtiefi:Illustrationofthebowtiefilterinthex-raybeamtoreduceth:Anexampleofnoise-equivalentnumberofx-rayquantacurvesfor140,120,100,and80kVthatcanbeusedforcharacterizingtheeffectofthenonuniformphotonintensitycausedbythebowtiefirrentmodulationonnoisecharacteristicsofCTdataisevenmoresignifiore,forsimplicity,weuseaphoton-countingmodelandwillconsidertheeffectofthebowtiefivenattenuatingpathintheimagedsubject,denotetheincidentandthepenetratedphotonnumbersasN0͑note␣,␯,␭͒andN͑theindexofdetector␣,␯,␭͒,respectively,wherebinsalongtheradial␣andandlongitu-vde-dinaldirections,and␭resenceofnoise,y,thelineintegralalongtheat-tenuatingpathisgivenbyP=−ln͑N/N0͒.Herein,weneglectthedetectorindex͑␣,␯,␭͒meneglecttheelec-tronicnoisberofinputphotonsN␭.0͑␣,␯,␭͒mustnowbeestimatedasafunctionof␣,␯,orationoftheeffectofx-raybeambowtiefilterTheincidentnumberofphotonsvariesforeachprojectionangleduetotheuseoftheautomaticexposurecontrol͑AEC͒technique22andisalsononuniformacrosstheradiationfieldofthex-raybeammainlyduetotheuseofthebeam-shapingbowtiefilter.23Toaccuratelyquantifythenoisepropertiesintheprojectiondataandpreservethenoisepatterninthede-noisedimage,skcansimplybeaccomplishedbyexpressingthein-cidentnumberofphotonsNontheestimation0asafunctionofdetectorbinindex␣andvbasedofthenonuniformityacrossthex-rayradiationfieldandafunctionofprojectionangle␭ninFig.1͑left͒,abowtiefiethecrosssectionofmostpatientsisovallyorcircularlyshaped,theatpose

4914Manducaetal.:Projectionspacedenoisingwithbilateralfiverepresentsthereferencesignals͑I0͒erencesignalispro-portecurrentoscillatesasthetabletranslatestoadapttothediffeowtiefilteristoreducetheincidentx-rayintensityintheperipheralregionsothattheradiationdosetothepatient,especiallytheskindose,se-quence,thex-rayintensityincidenttothepatientishighlynonuniformacrossthefanbeam,ricallydeter-minetheeffectofthebowtiefierseofthevari-anceisanumberthatcanbeusedtoestimatetheincidentx-rayintensityacrossthex-raybeam.21Figure1͑right͒dis-playsanexampleofthenoise-equivalentincidentquantanumberonasingledetectorrowacrossthex-raybeamob-tainedfordifferenttubepotentials͑kV͒.Byfittingthevari-ancewithathird-orfourth-orderGaussianequation,fourcalibrationcurvesoftheincidentx-rayintensityforthekVsat80,100,120,librationcurvesmaybedifferent,dependingontheconfiverepresentsthereferencesignalsofthetubeasafunctionofthetableposition,erencesignalispro-porteseen,thetubecurrentoscillatesduringthegantryrotationinordertoato-matictubecurrentmodulationleadstoacontinuouschangeintheincidentx-rayintensity,rporatethisef-fectbyextractingthereferencesignalfromeachprojectionMedicalPhysics,Vol.36,No.11,November20ibrationcurvesdeterminedfromthebowtiefiamsmoothingwithbilateralfilteringToincorporatethenoisemodelinbilateralfiltering,wefirstconvertthemeasuredsinogramPtoadatasetrepresent-ingamapofdetectednumberofphotons,whichissimplyexpressedasN=N0exp͑−P͒.͑7͒Practically,alnumberofincidentphotonsbeforetheattenuationN0canbeestimatedasthenoise-equivalentphotonnumber,combetransform24isastandardstatisticaltooltoconvertPoissondistributeddatatodatawithanapproximatelynormaldistri-butionwithaconstantvariance,Q=2ͱ͑N+3/8͒.͑8͒ThistransformationiimumfluxlevelsinCTdalsoignorethesmallconstantadditivefactorof3/8͑negligibleatthesecountnumbers,buteasilyincludedifdesired͒andthemul-tiplicativefactorof2,andsimplytakethesquarerootofthephotonnumbertogeneratethedatasetwhichissubsequentlyusedfordenoising,withaconstantstandarddeviationof1/are-root-transformeddataaregivenbyQ=ͱN=ͱN0exp͑−P͒.͑9͒Equation͑5͒canbeappliedonQtoobtainthedenoiseddatasetQˆ.ThestepsarethenreversedtoconvertQˆbacktothelog-transformedsinogram,tionofnoiseandresolutionpropertiesWeperformedphantomstudiestoevaluatethenoise-resolutionpropertiesofbilateralfitudieswereperformedonadual-sourceCTscanner͑SomatomDefinition,SiemensMedicalSolutions,Forchheim,Germany͒.Aphantomwithasmallacryliccyl-inderandathinwirethatistypicallyusedforqualitycontrolonSiemensscannerswasscannedwiththefollowingparam-eters:120kVp,0.5srotationtime,32ϫ0.6mm2detectorcollimation,672ϫ32detectormatrixsize,helicalpitchof1.0,geswererecon-structedusingaseriesofkernelsdataweredownloadedfromthescannerandde-noisedwithbilateralfissianfilterwithagivenspatialstandarddeviationdinEq.͑3͒wasapproxi-matedtoagivenfilterlengthw,andwefounditusefulempiricallytolocktheratioofdtowas1/oisingparameterswerefilterlengthw=5͑correspondingtod

4915Manducaetal.:ProjectionspacedenoisingwithbilateralfilteringinCT4915=5/6andevaluatedfromϪ2to2͒and␴ϭ0.7,1,1.4,1.8,2.2,exploreddifferentvaluesofwandfound,asexpected,thatlargerficereasons,weonlydiscussresultswithwfixedat5,-noiseddatawereuploadedtothescannerandreconstructedwithboththeB70fandB40fkernels͑theB70fkernelisanextremelysharpbutnoisykernel,whiletheB40fisslightlysharperandnoisierthanisusedatsomeinstitutions,butitisemployedinourclinicalpracticeforroutinebodyCT͒.Themodulationtransferfunction͑MTF͒oneachimage,eitherdirectlyreconstructedonthescannerorafterbilateralfilterdenoising,selevelatasmallregionofinterest͑ROI͒dphantomconsistedofastadium-shapedwatertank͑lateralwidthof30cm,heightof22.5cm͒.Eightthinplateswithdifferentcontrastlevels͑120HU:2;70HU:3;40HU:3͒wereplacedinthecentralregionnningparametersweredetectorcollimation64ϫ0.6withaz-flyingfocalspot,120qualityreferencemAs,rotationtimeof0.5s͑theterm“qualityreferencemAs”isusedintheueequalstheeffectivemAsusedforastandardpatientsize͒.TheimageswerereconstructedwithcommercialkernelsatB45,B40,B30,B20,datawerede-noisedwithw=5and␴ϭtioninCTcolonographyWeperformedapreliminarystudytoevaluatethenoise-resolutionpropertiesofbilateralfitedCTrawdatawereientwasscannedonthedual-sourceCTsystemwiththefollowingscanningparam-eters:120kVp,100qualityreferencemAs,0.5srotationtime,32ϫ0.6mm2detectorcollimation,umeCTdoseindex͑CTDIvol͒geswerereconstructedonthescannerwithaslicethick-nessof1mmandseveralreconstructionkernels͑B10f,B20f,B30f,andB40f͒dataweredownloadedfromtheCTscan-nerandprocessedwithbilateralfiotheddataweresubsequentlyre-loadedonthescannerandreconstructedwithaB40fkernel,tioninCTenterographyWeappliedbilateralfilteringtofiamwasscannedinadual-energymodewithonetubeoperatedat140kVandtheotherat80kV,sofimages͑lowandhighenergy͒lPhysics,Vol.36,No.11,-resolutionpropertiesofbilateralfisexpressedasthestandarddeviation͑HU͒tialresolutionwasquantifiedasthespatialfrequencyat10%idcurvelinkingthesolidtriangles͑᭡͒wasobtainedfromtheimagescannedwith40mAsandreconstructedwithkernelsofB10f,B20f,B30f,B40f,andB50f͑fromlefttoright͒.Thesoliddiamondsymbol͑ࡗ͒hedcurvelinkingtheopentriangles͑᭝͒representsthenoise-resolutionresultsobtainedfromimagesafterapplyingbilateralfifttoright,thefirstfivepointswererecon-structedwiththeB40fkernel,withwfixedat5,and␴ϭ2.2,1.8,1.4,1.0,0.7,respectively;thesecondfivepointswerereconstructedwithasharperB70fkernel,withwfixedat5,and␴ϭ2.8,2.2,1.8,1.4,and1.0,idcurvelinkingthesolidcircles͑b͒wasobtainedfromtheimagescannedwith80mAsandreconstructedwithkernelsofB10f,B20f,B30f,B40f,andB50f͑fromlefttoright͒.Thedashedcurvelinkingtheopencircles͑᭺͒representsthenoise-resolutionresultsobtainedfromimagesafterapplyingbilateralfiltse-resolutionresultsonthe40mAsdataafterbilateralfilteringapproachorexceedthenoise-resolutionproper-tiesofthe80mAsdata,andfisthedual-energyprocessing–28thatisusedtoprovidematerial-specificinformation,26thedual-energyimagesaremixedtogetherinalinearfashiontoformasinglesetofimages,whichservesasim80kVimagesobtainedfromadual-energyscanhaveenhancediodinesignalcomparedto140kV͑theiodinesig-nalisapproximatelydoubled͒.However,theyareoftensub-jecttoincreasedn-energyimagesaloneareofteninsufficiedbilateralfiltering͑w=5,␴ϭ1͒,followedbyB40freconstructiontothe80-resolutionpropertiesFigure3comparesthenoise-resolutionpropertiesofbilat-eralfiltesewasrepresentedbythestandarddeviation͑HU͒tialresolutionwasrep-resentedbythespatialfrequencyat10%idcurvelinkingthesolid

4916Manducaetal.:ProjectionspacedenoisingwithbilateralfilteringinCT4916triangles͑᭡͒wasobtainedfromtheimagescannedwith40mAsandreconstructedwithkernelsofB10f,B20f,B30f,B40f,andB50f͑fromlefttoright͒.Ascanbeseen,thesebodymootherkernel,thenoiselevelontheimageislower,iddiamondsymbol͑ࡗ͒wasfromthesamescanandrepresentsaspecialbodykernelB25f,whichinvolvesatwo-dimensionaladaptivefihedcurvelinkingtheopentriangles͑᭝͒representsthenoise-resolutionresultsobtainedfromimagesafterapplyingbilateralfifttoright,thefirstfivepointswerereconstructedwiththeB40fkernel,withwfixedat5,and␴ϭ2.2,1.8,1.4,1.0,0.7,respec-tively;thesecondfivepointswerereconstructedwithasharperB70fkernel,withwfixedat5,␴ϭ2.8,2.2,1.8,1.4,and1.0,idcurvelinkingthesolidcircles͑b͒wasobtainedfromtheimagescannedwith80mAsandreconstructedwithkernelsofB10f,B20f,B30f,B40f,andB50f͑fromlefttoright͒.Thedashedcurvelinkingtheopencircles͑᭺͒representsthenoise-resolutionresultsobtainedfromimagesafterapplyingbilateralfiltseethatamuchbetternoise-resolutiontrade-offisachievedbybilateralfilteringthanbythebodykernelsaloneonthe40mAs,withnoise-resolutionpropertiesap-proachingorexceedingtheconventionallyreconstructed80mAsdata͑withtwicetheradiationdose͒.Forexample,foragivennoiselevelof16HUonthe40mAsdata,bilateralfiltering͑w=5,␴ϭ1.4,B70frecon͒yieldsaspatialreso-lutionof7.7lp/cmat10%MTF,muchhigherthandoestheB40fkernelwithoutfiltering͑6.6lp/cm͒.Thisisalsely,atagivenresolution,bilateralfilteringof-fersmuchlowernoiselevels—e.g.,theB30fkernelaloneyieldsanoiselevelof13HUataresolutionof5.9lp/cm,whilebilateralfiltering͑w=5,␴ϳ0.7,B40frecon͒wouldgiveanoiselevelof8HUatthisresolution,se-resolutionresultsonthe40mAsdataafterbilateralfilteringapproachorexceedthenoise-resolutionpropertiesoftheun-fiarimprovementinthenoise-resolutiontrade-offisobtainedbyfiallydemonstratetheimprovementofspatialreso-lution,thepointspreadfunctions͑PSFs͒forthewireimagesobtainedwithbilateralfiltering͑w=5,␴ϭ1.4,B70frecon͒andtheunfiageshaveasimilarnoiselevelof16HU,butthebilateralfilteredimagehasasharperapp5showstheimagesforthestadium-shapedphan-tomandblowupsofthecentralregioncontainingthecontrastplatesafterB45reconstruction͑leftcolumn͒,bilateralfilter-ingfollowedbyB45reconstruction͑center͒,andB20recon-struction͑right͒.ThestandarddeviationsinsidetheROIare49.1,31.9,and32.9HU,etheapproxi-MedicalPhysics,Vol.36,No.11,November225200450500w=5,σ=1.4,B70f,FOV=50mmB40f,FOV=50mm55520w=5,σ=1.4,B70f,FOV=5mmB40f,FOV=hewireimagesobtainedwithbilateralfiltering͑w=5,␴͑rightϭ1.4͒displayed͒withtheinB70fanlargekernelFOV͑leftof͒50andmmthe͑topB40frowkernel͒andwithoutasmallfilteringFOVof5mm͑bottomrow͒.Theimageshavethesamenoiselevelat16HU,whiletheimagewithbilateralfilteringhasamuchsharperappmatchednoiselevels,thelowercontrastplatesare,inouropinion,tionofnoise-resolutionpropertiesinCTcolonographyFigure6͑a͒showsasliceofthenoncatharticCTcolonog-raphydatacontainingbarium-taggedstoolreconstructedwithastandardB40freconstructionkernel͑a͒,withthesamekernelafterbilateralfiltering͑b͒withw=5,␴ϭ1.1,͑c͒andwiththeunfi͑b͒and͑c͒gesforthestadium-shapedphantomafterB45reconstruc-tion͑topleft͒,bilateralfilteringfollowedbyB45reconstruction͑topcenter͒,andB20reconstruction͑topright͒.ndarddeviationsinsidetheROIare49.1,31.9,and32.9HU,ercontrastplatesare,inouropinion,bettervisualizedwiththedenoisedimagethanwiththeB20fimage.

4917Manducaetal.:Projectionspacedenoisingwithbilateralfiofthecoloncontaininglabeledstool͑a͒withstandardB40freconstructionkernelandalineprofileacrossstool-airinterface,͑b͒withB40freconstructionafterprojectionspacebilateralfilteringwithw=5,␴ϭ1.1,and͑c͒reconstructedwiththeunfilteredB10fkernel.͑d͒Aprofilealongthelineindicatedin͑a͒,showingthevalues͑unitsofHUϩ1024͒fortheB40f͑᭺͒,B40fwithdenoising͑ᮀ͒,andB10f͑᭡͒.͑e͒DifferenceimagebetweenB40fandB40fwithdenoisingreconstructions.͑f͒rnoiselevelsinanROIinthelumen͑14.5and14.7,respectively͒.Profilesalongthestool-airboundary͑d͒showthatthedenoisedB40fimagehasasharperstool-airtransi-tionthantheB10f,whiledifferenceimages͑e͒and͑f͒showthattitativelyevaluatetheresolutionpropertyofeachreconstruction,weusedtheprofileacrosstheboundarybe-tweenthelabeledstoolandairshowninFig.6͑a͒.Thegra-dientoftheprofilewascalculatedandthemaximumnega-tivegradientvaluewasusedforcomparinseinanearbyairregion͑insidethelumen͒7displaystheplotofnoiselevelversusspatialresolution͑representedbythemaximumnegativegradientvalue͒forvariousreconstructionkernelsandforbilateralfilteringwithw=5anddifferent␴settings,eseenthatbilateralfilteringcanreducenoil-lowedwithaB40freconstruction,forexample,bilateralfil-teringwith␴of0.5canachievealowernoiselevelthananunfilteredB30freconstruction,butwithbetterresolution,whilefilteringwith␴of0.7reducesnoisetotheleveloftheunfilteredB20freconstructionwithresolutionstillslightlybetterthananunfiralfilter-ingwith␴of1.1givesslightlylowernoisethantheunfil-MedicalPhysics,Vol.36,No.11,November2009teredB10freconstructionbutwithsignificantlybetterreso-lution͑thesearetheimagesshowninFig.6͒.tionofnoise-resolutionpropertiesinCTenterographyFigure8disprightimagewasreconstructedwiththesamekernelafterbilateralfiltering͑w=5,␴ϭ1͒.selevelsintheROIdenotedbythecircleare39.1,25.6,and25.9,fileatthebottomrightshowsthatthedenoisedB40fisslightualizationofthemuralstratificationanddeli-nationoftheinnerandouterboundariesoftheneoterminalileum͑arrow͒hasbeenimprovedbybilateralfiltering,rresultswereobtainedinCTdatasetsvisualizingthebowel͑n=2͒,pancreas͑n=2͒,andliver͑n=1͒.Ineachcase,aboard-certifiedsubspecializedradiologistratedthedenoised80kVimagesmarkedlysuperiorinimagequalitycompar5/5cases,denoisingimprovedim-agequalitytothepointwherethe80kVimagesalonewere

4918Manducaetal.:ProjectionspacedenoisingwithbilateralfirddeviationofnoiseinairROIvslargestnegativegradientinprofileinFig.6͑a͒calculatedfordifferentreconstructionkernelsandfordifferentlevelsofbilateralfiidcurvelinkingthesolidtriangles͑᭡͒wascalculatedfromimagesreconstructedwithkernelsofB40f,B30f,B20f,andB10f͑fromlefttoright;notethatsharperedgesaretotheleft͒.Thedashedcurvelinkingthecircles͑b͒wascalculatedfromimagesreconstructedwiththeB40fkernelafterdenoisingwithw=5and␴ϭ0.3,0.5,0.7,0.9,1.1,and1.5,eredtobeofdiagnosticquality͑currentlythemixedimages,withtwicetheradiationdose,areusedforthispur-pose͒.SIONSWeinvestigatedanoniterativeapproachtoreducingnoiseinCTusinglocallyadaptivebilateralsinogramfilteringwithaCTnoisemodelthatincludedtheeffectsofthebowtiefifilteringcanbeimple-mentedverysimplyandmoreeffiuatedtheresolution-noisepropertiesofbilateralfilteringwiultsdemonstratethatitcanachieveabetternoise-resolutisereductionshouldbetrans-latabletoimprovementsinimagequalityand/ctthismethodtohavedifficultywithsmall,low-contrastobjectsandwithsubtletexturewithintensitynearthenoiselevel,hodmightalsobeexpectedtocauseaslightlossofresolutionintheslicedirection,althoughitcouldbearguedthattheedge-preservingnatureofthefilter-ingmightyieldabetternoise-resolutiontrade-offinzthanthefighevaluationsagainstotherexistingsinogramdenoisingmethodsarere-quired,butthesimplicityandeffectivenestionsarealsorequiredonspecificdiagnostictaskstoestablishthepossiblebenefitsofthisdenoisingapproachandMedicalPhysics,Vol.36,No.11,st-enht:erepresentstheprofiht:Imageafterbilateralfilteringandreconstruction͑w=5,␴ϭ1,B40f͒.Radiologistspreferredthevisualizationofthemuralstratificationintheneoterminalileum͑arrow͒left:selevelsintheROIdenotedbythecirclewere39.1,25.6,and25.9,right:ProfilesacrossthelineintheupperleftshowingthevaluesfortheB40f͑᭺͒,B40fwithdenoising͑ϩ͒,andB20f͑᭡͒rethatchangesinthetexturalappearanceoftheim-ages͑whichwilloccurwithanydenoisingalgorithm͒donotimpedediagnosticperformance.a͒onicmail:manduca@;Presentaddress:200FirstStreetSW,Rochester,1MN55905;Telephone:͑507͒284-8163;Fax:͑507͒,“Computedtomography—anincreasing2sourceofradiationexposure,”.357,2277–2284͑2007͒.,“Patientradiationdosesfromadultandpediatric3CT,”AJR,enol.188,540–546͑2007͒.,PrinciplesofComputedTomographicImaging4͑SIAM,Philadelphia,PA,2001͒.,“Adaptivestreakartifactreductionincomputedtomographyresultingfromexcessivex-rayphotonnoise,”.25,2139–21475͑1998͒.riess,,ar,“Generalizedmulti-dimensionaladaptivefilteringforconventionalandspiralsingle-slice,6multi-slice,andcone-beamCT,”.28,475–490͑2001͒.,,,,,,,“Nonlinearsinogramsmoothingforlow-dosex-rayCT,”.51,72505–2513͑2004͒.,,,,“Penalizedweightedleast-squaresapproachtosinogramnoisereductionandimagereconstructionforlow-dosex-raycomputedtomography,”g25,1272–81283͑2006͒.ère,“Penalized-likelihoodsinogramsmoothingforlow-dose9CT,”.32,1676–1683͑2005͒.ère,,,“Penalized-likelihoodsinogramrestorationforcomputedtomography,”g25,101022–1036͑2006͒.lt,,,,“Athree-dimensionalstatisticalapproachtoimprovedimagequalityformultislice11helicalCT,”.34,4526–4544͑2007͒.C.-,field,ao,,t,s,“TensorcontrolledlocalstructureenhancementofCTimagesforbonesegmentation,”ProceedingsofMICCAI1998͓.

4919Manducaetal.:ProjectionspacedenoisingwithbilateralfilteringinCT4919121496,1205–1212͑1998͔͒.er,rger,h,mmer,nbeck-Regn,,“Spatialdomainfilteringforfastmodi-ficationofthetradeoffbetweenimagesharpnessandpixelnoiseincom-13putedtomography,”g22,846–853͑2003͒.,,h,,,,“Effectofnonlinearthree-dimensionaloptimizedreconstructionalgo-rithmfilteronimagequalityandradiationdose:Validationonphantoms,”.36,95–97͑2009͒.hi,“Bilateralfilteringforgrayandcolorim-ages,”presentedatIEEEInternationalConferenceonComputerVision,15Bombay,India,1998͑unpublished͒.,“Scale-spaceandedgedetectionusinganisotropic16diffusion,”.12,629–639͑1990͒.,“Ontheoriginofthebilateralfilterandwaystoimproveit,”rocess.11,1141–1151͑2002͒.aya,“Reductionofnoiseandimageartifactsincomputedto-mographybynonlinearfiltrationofprojectionimages,”4322,18917–923͑2001͒.et,“Separablebilateralfilteringforfastvideopreprocessing.”ProceedingsofIEEEInternationalConferenceonMulti-19mediaandExpo,Amsterdam,6–8July2005͑unpublished͒,,FoundationsofImageScience͑Wiley,20NewYork,2004͒.,“Imagecovarianceandlesiondetectabilityindirectfan-beamx-raycomputedtomography,”.53,MedicalPhysics,Vol.36,No.11,November20092471–2493͑2008͒.g,mzadeh,,J.A.O’Sullivan,,“Propertiesofpreprocessedsinogramdatainx-raycomputedtomography,”.33,3290–3303͑2006͒.er,,,“mmeasurements,”.26,2248–2253͑1999͒.,ComputedTomography:Principles,Design,Artifacts,andRe-centAdvances͑SPIE,Bellingham,WA,2006͒.be,“ThetransformationofPoisson,binomialandnegative-binomialdata,”Biometrika15,246–254͑1948͒.,“DeterminationofthepresampledMTFincomputedtomog-raphy,”.28,356–360͑2001͒.n,,ir,ck,,d,,ch,d,t,,,,“MaterialdifferentiationbydualenergyCT:Initialexperience,”.17,1510–1517͑2007͒.el,ann,felder,ler,lles,a,ek,i,“Dual-energycontrast-enhancedcomputedtomographyforthedetectionofurinarystonedisease,”.42,823–829͑2007͒.,er,a,k,,n,ms,Jr.,ough,“Noninvasivedifferentiationofuricacidversusnon-uricacidkidneystonesusingdual-energyCT,”.14,1441–1447͑2007͒.