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1、IterativeMethodsforImageReconstructionTheseannotatedslideswerepreparedbyJeffFesslerforattendeesoftheISBItutorialonstatisti-calimagereconstructionmethods.Thepurposeoftheannotationistoprovidesupplementaldetails,andparticularlytoprovideex-tensiveliteraturereferencesforfurthe
2、rstudy.JeffreyA.FesslerForafascinatinghistoryoftomography,see[1].Forbroadcoverageofimagescience,see[2].Forfurtherreferencesonimagereconstruction,seereviewpapersandchapters,e.g.,[3–9].EECSDepartmentTheUniversityofMichiganISBITutorialApr.6,20060.00.0cJ.Fessler,March15,2006p
3、0introImageReconstructionMethods(SimplifiedView)AnalyticalIterative(FBP)(OSEM?)(MR:iFFT)(MR:CG?)0.10.1cJ.Fessler,March15,2006p0introImageReconstructionMethods/AlgorithmsPartofthegoalistobringordertothisalphabetsoup.ANALYTICALITERATIVEFBPBPFAlgebraicStatisticalGridding(y=Ax
4、)...ART(Weighted)LikelihoodMARTLeast(e.g.,Poisson)SMARTSquares...EM(etc.)CGOSEMCDSAGEISRACG...Int.PointGCAPSCDFSCD...0.20.2cJ.Fessler,March15,2006p0introOutlineofPartIEmphasisongeneralprinciplesratherthanspecificempiricalresults.Part0:Introduction/Overview/ExamplesThejourn
5、als(andconferenceslikeNSS/MIC!)arerepletewithempiricalcomparisons.Part1:ProblemStatementsAlthoughthefocusofexamplesinthiscoursearePET/SPECT/CT,mostoftheprinciples◦Continuous-discretevscontinuous-continuousvsdiscrete-discreteapplyequallywelltoothertomographyproblemslikeMRi
6、magereconstruction,optical/diffractionPart2:FourofFiveChoicesforStatisticalImageReconstructiontomography,etc.◦Objectparameterization◦Systemphysicalmodeling◦Statisticalmodelingofmeasurements◦CostfunctionsandregularizationPart3:FifthChoice:Iterativealgorithms◦Classicaloptim
7、izationmethods◦Considerations:nonnegativity,convergencerate,...◦Optimizationtransfer:EMetc.◦Orderedsubsets/blockiterative/incrementalgradientmethodsPart4:PerformanceAnalysis◦Spatialresolutionproperties◦Noiseproperties◦Detectionperformance0.30.3cJ.Fessler,March15,2006p0int
8、roHistoryBracewell’sclassicpaperondirectFourierreconstructionalsomentionsasuccessivesubstitution
