# Computed Tomography Principles

## Presentation on theme: "Computed Tomography Principles"— Presentation transcript:

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) (on-line slides & handouts in the Teaching section)