TheFilteredBackprojectionAlgorithminMATLAB,GregGallardo51:185,FilteredBackprojectionAlgorithm,MeasurethefamilyofprojectionsK=#ofprojections(angles),N=#ofrays(detectorsize)PerformFFTMultiplyFFTbyFFT.PerformIFFTproductfromstep3Performbackprojectionas:,1)Measurethefamilyofprojections,R,Xp=RADON(.)returnstwovariablesMatrixRcolumnsaretheRadontransformfortheangles.RowsaredetectorpositionVectorXp-containingtheradialcoordinatescorrespondingtoeachrowofR.,1)Measurethefamilyofprojections,Functionparameterssize():getsNandKnextpow2():getwidthforFFT,2)PerformFFT,MATLABstandsforMATrixLABoratoryMatrixoperationsarefasterthanvisitingeachelementinaloop.,3)MultiplyFFTbyFFT,BackprojectionfiltersShepp-Logan:Ram-Lakmultipliedbysincfunction(seeiradonhelp)Cosine:Ram-LakmultipliedbycosineHamming:Ram-LakmultipliedbyHammingwindowHanning,Blackman,etc.,3)MultiplyFFTbyFFT,Ram-Lak,Shepp-LoganandCosinefiltersinfrequencydomain,3)MultiplyFFTbyFFT,FIRFilters.CommonlyusedWindows,Figurefrom“Discrete-TimeSignalProcessing”,Oppenheim&Schafer,Prentice-Hall,3)MultiplyFFTbyFFT,RectangularBartlett(triangular)Hanning(vonHann)HammingBlackman,from“Discrete-TimeSignalProcessing”,Oppenheim&Schafer,Prentice-Hall,3)MultiplyFFTbyFFT,3)MultiplyFFTbyFFT,3)MultiplyFFTbyFFT,Filterstep.Elementbyelementmultiplication,4)IFFTproductfromstep3,5)PerformBackprojectionas:,Results,Results,