MATLAB实现的医学图像FBP算法

TheFilteredBackprojectionAlgorithminMATLABGregGallardo51:185FilteredBackprojectionAlgorithm1.MeasurethefamilyofprojectionsK=#ofprojections(angles),N=#ofrays(detectorsize)2.PerformFFT[]3.MultiplyFFT[]byFFT[].4.PerformIFFT[productfromstep3]5.Performbackprojectionas:NnKinPi,...,2,1;,...,2,1,KinPi,...,2,1,nPinhKiiiyxQKyxfi1sincos,1)Measurethefamilyofprojections[R,Xp]=RADON(...)returnstwovariablesMatrixR–columnsaretheRadontransformfortheangles.RowsaredetectorpositionVectorXp-containingtheradialcoordinatescorrespondingtoeachrowofR.1)MeasurethefamilyofprojectionsFunctionparameterssize():getsNandKnextpow2():getwidthforFFT2)PerformFFT[]MATLABstandsforMATrixLABoratoryMatrixoperationsarefasterthanvisitingeachelementinaloop.KinPi,...,2,1,3)MultiplyFFT[]byFFT[]BackprojectionfiltersShepp-Logan:Ram-Lakmultipliedbysincfunction(seeiradonhelp)Cosine:Ram-LakmultipliedbycosineHamming:Ram-LakmultipliedbyHammingwindowHanning,Blackman,etc.nhnPi3)MultiplyFFT[]byFFT[]Ram-Lak,Shepp-LoganandCosinefiltersinfrequencydomainnhnPi3)MultiplyFFT[]byFFT[]FIRFilters.CommonlyusedWindowsnhnPiFigurefrom“Discrete-TimeSignalProcessing”,Oppenheim&Schafer,Prentice-Hall3)MultiplyFFT[]byFFT[]RectangularBartlett(triangular)Hanning(vonHann)HammingBlackmannhnPiotherwiseMnnw,0,0,1][otherwiseMnMMnMnMnnw,02/,/222/0,/2][otherwiseMnMnnw,0,0),/2cos(5.05.0][otherwiseMnMnnw,0,0),/2cos(46.054.0][otherwiseMnMnMnnw,0,0),/4cos(08.0)/2cos(5.042.0][from“Discrete-TimeSignalProcessing”,Oppenheim&Schafer,Prentice-Hall3)MultiplyFFT[]byFFT[]nhnPi3)MultiplyFFT[]byFFT[]nhnPi3)MultiplyFFT[]byFFT[]Filterstep.ElementbyelementmultiplicationnhnPi4)IFFT[productfromstep3]5)PerformBackprojectionas:KiiiyxQKyxfi1sincos,ResultsResults