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Computed TomographyComputed Tomography
ReferencesReferences
The Essential Physics of Medical Imaging 2The Essential Physics of Medical Imaging 2ndnd ed ednn..
Bushberg J.T. et.alBushberg J.T. et.al
Computed Tomography 2Computed Tomography 2ndnd ed ednn : Seeram : Seeram
Physics of Radiology : Wolboarst A.B.Physics of Radiology : Wolboarst A.B.
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COMPUTED TOMOGRAPHYCOMPUTED TOMOGRAPHY
Invented by Godfrey Hounsfield in 1971Invented by Godfrey Hounsfield in 1971
Won the Nobel Prize in Medicine in 1979 Won the Nobel Prize in Medicine in 1979 shared with Alan Cormackshared with Alan Cormack
Alan Cormack developed the image Alan Cormack developed the image reconstruction method in CTreconstruction method in CT
Radon developed the mathematical Radon developed the mathematical principles of CT in 1917principles of CT in 1917
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Computed TomographyComputed Tomography
Produces a cross sectional image of linear Produces a cross sectional image of linear
attenuation coefficients of a slice of tissueattenuation coefficients of a slice of tissue
by measuring the transmitted x-ray by measuring the transmitted x-ray intensity through the sliceintensity through the slice
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eII yxlyxt
),(),(0
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Hounsfield ScannerHounsfield Scanner
160 measurements during translation160 measurements during translation
180 angular positions180 angular positions
Image size = 80Image size = 80x80 = 6400 unknownsx80 = 6400 unknowns
Number of equations = 160x180=28800Number of equations = 160x180=28800
Number of equations > Number of Number of equations > Number of unknowns, Solution is possibleunknowns, Solution is possible
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Tomographic Reconstruction MethodsTomographic Reconstruction Methods
Filteredback Projection MethodFilteredback Projection Method
Direct Fourier Transform MethodDirect Fourier Transform Method
Iteration MethodIteration Method
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Back Projection MethodBack Projection Method
Projection elements are divided uniformly Projection elements are divided uniformly amongst pixels in projection pathamongst pixels in projection path
Non zero activity outside the true location Non zero activity outside the true location of the objectof the object
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Filtered Back ProjectionFiltered Back Projection
Acquire projection profiles at N projection Acquire projection profiles at N projection anglesangles
Do 1D FT of each profileDo 1D FT of each profile
Filter each k space profileFilter each k space profile
Inverse FT each filtered profile to obtain Inverse FT each filtered profile to obtain filtered profile in space domainfiltered profile in space domain
Back project the filtered profileBack project the filtered profile
FBP is the most widely used FBP is the most widely used reconstruction method in CTreconstruction method in CT
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Image reconstructionImage reconstruction
Filtered back projection of the data Filtered back projection of the data corresponding to a single slice produces corresponding to a single slice produces the image of that slice.the image of that slice.
Repeating the above procedure for all Repeating the above procedure for all slices gives the 3D image.slices gives the 3D image.
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