Computed Tomography Principles Ge Wang, Ph.D. Department of Radiology University of Iowa Iowa City, Iowa 52242, USA
Learning Objectives CT terms Data acquisition Basic elements of CT scanner Scanning modes Image reconstruction Spiral/helical CT Image resolution and artifacts Interaction among imaging parameters Quality assurance Radiation exposure
A Little Bit History Nobel prizes Roentgen (1901): Discovery of X-rays Hounsfield & Cormack (1979): Computed tomography
Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction
X-ray Interactions - Photoelectric Effect (From Aracor) Photoelectric effect results in total absorption of the X-ray photon and the emission of a bound electron
X-ray Interactions - Compton Scatter (From Aracor) Compton Scatter results in a free electron & a scattered (less energetic) photon
Source and Detectors Source - Rotating anode disk - Small focal spot down to 0.6 mm - Polychromatic beam Detectors - Xenon (50-60%) - Scintillation (>90%) (From Siemens)
Exponential Attenuation of X-ray Ni No m Ni: input intensity of X-ray No: output intensity of X-ray m: linear X-ray attenuation x Ni No x Attenuated more X-rays
Ray-Sum of X-ray Attenuation Ni No k x Ray-sum Line integral
Projection & Sinogram y P(t) t p x f(x,y) t X-rays Sinogram Projection: All ray-sums in a direction Sinogram: All projections y P(t) t p x f(x,y) t X-rays Sinogram
Completeness Condition There exists at least a source on any line intersecting a cross-section
Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction
First Generation One detector Translation-rotation Parallel-beam
Second Generation Multiple detectors Translation-rotation Small fan-beam
Third Generation Multiple detectors Translation-rotation Large fan-beam
Fourth Generation Detector ring Source-rotation Large fan-beam
Third & Fourth Generations (From Picker) (From Siemens)
Spiral/Helical Scanning Simultaneous Source rotation Table translation Data acquisition
Cone-Beam Geometry
Scanning modes First generation One detector, translation-rotation Parallel-beam Second generation Multiple detectors, translation-rotation Small fan-beam Third generation Multiple detectors, rotation-rotation Large fan-beam
Scanning modes Fourth generation Detector ring, source-rotation Large fan-beam Spiral/Helical scanning, cone-beam geometry
Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction
Spiral CT Scanner Network Gantry Source Computer Parallel processor Display Control console Table Recording Detectors Data acquisition system Storage units: Tapes, disks
Data Acquisition System (DAS) Pre-Collimator Post-Collimator Scattering Source Detector Filter Patient
Data Acquisition System (DAS) X-ray Tube Source Filter Detectors CT Gantry (From Siemens) Detector
Spiral CT Scanner Gantry Data acquisition system Table Computer Parallel processors Control console Storage units Tapes, disks Recording device Network interface X-ray generator Heat exchanger (From Elscint)
E-Beam CT Scanner Speed: 50, 100 ms Thickness: 1.5, 3, 6, 10 mm ECG trigger cardiac images (From Imatron)
Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction
Computed Tomography y Computed tomography (CT): Image reconstruction from projections t P(t) P(t) f(x,y) x f(x,y) X-rays
Reconstruction Idea =4 2=3 3=2 4=1
Algebraic Reconstruction Technique (ART) 3 2 4 1 6 -2 Update a guess based on data differences Guess 1 Guess 0 Guess 2 Error
Fourier Transformation f(x,y) F(u,v) Fourier Transform Image Space Fourier Space
Fourier Slice Theorem y P(t) v t F[P(t)] u x F(u,v) f(x,y) X-rays v F[P(t)] u F(u,v)
From Projections to Image y x v u F-1[F(u,v)] f(x,y) P(t) F(u,v)
Filtered Backprojection f(x,y) P(t) P’(t) 1) Convolve projections with a filter 2) Backproject filtered projections
Example: Projection Projection Projection Sinogram Ideal Image
Example: Backprojection
Example: Backprojection Sinogram Backprojected Image
Example: Filtering Sinogram Filtered Sinogram
Example: Filtered Backprojection Filtered Sinogram Reconstructed Image
References T. S. Curry III, J. E. Dowdey, R. C. Murry Jr. Christensen’s physics of diagnostic Radiology (4th edition), Lea & Febiger (for residents) G. Wang, M. W. Vannier: Computerized tomography. Encyclopedia of Electrical and Electronics Engineering, edited by Webster JG, to be published by John Wiley & Sons (for engineers) http://dolphin.radiology.uiowa.edu/ge (on-line slides & handouts in the Teaching section)