cosh-hilbert变换反演的矩方法及其在单光子发射计算机断层成像中的应用

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1、第30卷第6期计算物理V01．3O．No．62013年11月CHINESEJOURNAL0FCOMPUTATIONALPHYSICSNov．，2013ArticleID：1001-246X(2013)06-0799-09Moment．．basedCosh-HilbertInversionandApplicationsinSinglePhotonEmissionComputedTomography————一一LUOShousheng，YANGJiansheng，ZHOUTie(LMAM，SchoolofMathemati

2、calSciences，PekingUniversity，Beng100871，China)Abstract：BasedonTficomiformulaforHilberttransformandTaylorexpansionofcosh—function，anumericalinversionalgorithmforcosh—Hilberttransform(CHT)isproposedandappliedtosinglephotonemissioncomputedtomographyimaging．CHTofafu

3、nctionisrepresentedasitsHilberttransformandacorrectiontermincludingallofitsmomentsbyusingTaylorexpansionofcosh—function．AlinearsystemaboutallmomentsofthefunctionisobtainedviaTricomiformula．Finitenumbersofmomentscanbesolvedbytruncatingtheinfinitelinearsystem．andt

4、hefunctioncanbereconstructedapproximately．Numericalsimulationsareperformedtoverifythealgorithmbycomparingwithanalytiealinversionformula．Keywords：SPECT；coshHilberttransform；momentmethodCLCnumber：R814．4Documentcode：A0IntroductionSingle。photonemissioncomputedtomogr

5、aphy(SPECT)isanon-invasivediagnostictechnologyinnuclearmedicine．Itisusedtoimagethephysiologicalfunctioninformationofvariousorganswiththehelpofradiopharmaceutical，abiochemicalmolecularlabeledbyradioisotope．Radiopharmaceuticalisinducedintoapatient，andtheemittedgam

6、maphotons，attenuatedbythebody，aremeasuredbyagammacamerarotatingaroundit．ThetaskofSPECTimagereconstructionistoestimatetheradiopharmaceuticaldistributionfromthemeasureddata．Fromthemathematicalpointofview，thetwo-dimensional(2D)SPECTimagereconstructionproblemistoinv

7、erttheattenuatedRadontransform(aRt)ofp，g(s，咖)=Rp(s，咖)=上p(s+tO)exp(J=(s+f)dr)d，(1)where0=(COS，sin咖)and0：(一sin咖，COS咖)denotetwoperpendicularvectors，P(x)and(x)denoteradiopharmaceuticaldistributionandattenuationcoefficientofgammaphotonatx=(t，2)．AlthoughPisafunctionwi

8、thacompactsupport力inpractice，theintegral(1)iswrittenover(一∞，+∞)forconvenience．Afiheredback—projectionformulaforaRtwasdiscoveredbyNovikov(Later，asimplerderivationwasil