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.

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

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

eII yxlyxt

),(),(0

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

Tomographic Reconstruction MethodsTomographic Reconstruction Methods

Filteredback Projection MethodFilteredback Projection Method

Direct Fourier Transform MethodDirect Fourier Transform Method

Iteration MethodIteration Method

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

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

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.