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Binarytomographicimagereconstruction000
a)
b)
Figure101:Schematicdiagramofthescanningsystem:a)boreholetomography,b)
limited-viewparallel-beamX-raytomography
Theproblemsofimagereconstructioninlimited-datatomographyhavebeen
discussedbymanyresearchers.HansonandWecksung[25]reportedthatthe
limited-angleimagereconstructioncanbesignificantlyimprovedbyincorporating
apriorinformationaboutthetrueimagetotheinversemodelusingtheBayesian
framework.Thepriorinformationcanbeformulatedintermsofconstraintssuch
assparsity,smoothness,nonnegativity,boundness,binarityorunimodality.This
approachhasbeenalsojustifiedbytheoreticalconsiderationsin[66],whereYeet
aldemonstratedthatevenanexactimagereconstructionispossiblefromlimited-
angleprojections,providedthatthesufficientpriorinformationisincorporated.
Motivatedbythelevelsetmethods,Kolehmainenetal[33]proposedanew
methodforlimited-dataX-raytomographythatreduceslimited-angleartifactsby
constrainingthereconstructionwithanonlinearevolutionfunction.Thebox-like
constrainingstrategy[34]hasbeenalsoappliedbyPopaandZdunek[48]toa
familyoftheKaczmarzalgorithm[31]forboreholeimagereconstruction.The
constrainsbyhyperstripsintheKaczmarzalgorithmareappliedbyVishnyakov
andMashevskayain[63].SmoothnessconstraintscanbemodeledbytheMarkov
RandomField(MRF)modelorTotalVariation(TV)term.
TheconstraintsbasedontheMRFandincorporatedwiththeBayesianframe-
worktotheKaczmarzalgorithmareproposedin[47].Thelimited-dataim-
agereconstructionthatinvolvestheminimizationoftheTVtermisdiscussed
in[15,43,56,57,62].Assumingsparseinhomogeneousfeaturesintheimage,the
artifactscausedbylimited-anglescanningcanbereducedwithsparsityconstraints
suchasL1-norm[69].Rantalaetal[50]proposedtorepresenttheunknownimage
intheWaveletdomain,andtoincorporatethepriorknowledgebytheBesovspace
priortogetherwithpositivityconstraint.
Anotherapproachtotheartifactreductionistoperformthesegmentationof
