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Computed Tomography Principles Ge Wang, Ph.D. Department of Radiology University of Iowa Iowa City, Iowa 52242, USA.

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Presentation on theme: "Computed Tomography Principles Ge Wang, Ph.D. Department of Radiology University of Iowa Iowa City, Iowa 52242, USA."— Presentation transcript:

1 Computed Tomography Principles Ge Wang, Ph.D. Department of Radiology University of Iowa Iowa City, Iowa 52242, USA

2 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

3 A Little Bit History Nobel prizes Roentgen (1901): Discovery of X-rays Hounsfield & Cormack (1979): Computed tomography

4 Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction

5 X-ray Interactions - Photoelectric Effect Photoelectric effect results in total absorption of the X-ray photon and the emission of a bound electron (From Aracor)

6 X-ray Interactions - Compton Scatter Compton Scatter results in a free electron & a scattered (less energetic) photon (From Aracor)

7 Source - Rotating anode disk - Small focal spot down to 0.6 mm - Polychromatic beam Detectors - Xenon (50-60%) - Scintillation (>90%) Source and Detectors (From Siemens)

8 Exponential Attenuation of X-ray x NoNo NiNi x X-rays Attenuated more NoNo NiNi N i : input intensity of X-ray N o : output intensity of X-ray : linear X-ray attenuation

9 Ray-Sum of X-ray Attenuation x NoNo NiNi Ray-sum Line integral

10 Projection & Sinogram Sinogram t Sinogram: All projections P( t) f(x,y) t y x X-rays Projection: All ray-sums in a direction

11 Completeness Condition There exists at least a source on any line intersecting a cross-section

12 Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction

13 First Generation One detector Translation-rotation Parallel-beam

14 Second Generation Multiple detectors Translation-rotation Small fan-beam

15 Third Generation Multiple detectors Translation-rotation Large fan-beam

16 Fourth Generation Detector ring Source-rotation Large fan-beam

17 Third & Fourth Generations (From Picker) (From Siemens)

18 Simultaneous Source rotation Table translation Data acquisition Spiral/Helical Scanning

19 Cone-Beam Geometry

20 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

21 Scanning modes Fourth generation Detector ring, source-rotation Large fan-beam Spiral/Helical scanning, cone-beam geometry

22 Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction

23 Spiral CT Scanner Gantry Data acquisition system Detectors Storage units: Tapes, disks Display Control console Computer Parallel processor Table Recording Source Network

24 Filter Data Acquisition System (DAS) Source Detector Pre-CollimatorPost-Collimator Patient Scattering

25 Data Acquisition System (DAS) X-ray Tube Detectors CT Gantry (From Siemens) Filter Source Detector

26 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)

27 E-Beam CT Scanner Speed: 50, 100 ms Thickness: 1.5, 3, 6, 10 mm ECG trigger cardiac images (From Imatron)

28 Computed Tomography Principles 1. Projection measurement 2. Scanning modes 3. Scanner systems 4. Image reconstruction

29 Computed Tomography P( t) f(x,y) P( t) f(x,y) t y x X-rays Computed tomography (CT): Image reconstruction from projections

30 Reconstruction Idea

31 Algebraic Reconstruction Technique (ART) Update a guess based on data differences Guess 1 Guess 0 Guess 2 Error

32 Fourier Transformation Fourier Transform f(x,y) F(u,v) Image Space Fourier Space

33 Fourier Slice Theorem v u F(u,v) P( t) f(x,y) t y x X-rays F[P( t)]

34 From Projections to Image y x v u F -1 [F(u,v)] f(x,y) P( t) F(u,v)

35 Filtered Backprojection f(x,y) P( t) 1) Convolve projections with a filter 2) Backproject filtered projections

36 Example: Projection Sinogram Ideal Image Projection

37 Example: Backprojection Projection

38 Example: Backprojection SinogramBackprojected Image

39 Example: Filtering Filtered SinogramSinogram

40 Example: Filtered Backprojection Filtered Sinogram Reconstructed Image

41 References T. S. Curry III, J. E. Dowdey, R. C. Murry Jr. Christensens 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)


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