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Literature Review Single-Slice Rebinning Method for Helical Cone-Beam CT Fr d ric Noo, Michel Defrise, Rolf Clackdoyle Physics in Medicine and Biology – PowerPoint PPT presentation

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Title: Literature%20Review


1
Literature Review
  • Single-Slice Rebinning Method for
  • Helical Cone-Beam CT
  • Frédéric Noo, Michel Defrise, Rolf Clackdoyle
  • Physics in Medicine and Biology
  • Vol 44, 1999

Henry Chen May 13, 2011
2
Background
  • Computed Tomography

3
Tomography
  • Basis for CAT scan, MRI, PET, SPECT, etc.
  • Greek tomos part or section
  • Cross-sectional imagingtechnique using
    transmissionor reflection data frommultiple
    angles

4
Computed Tomography (CT)
  • A form of tomographic reconstruction on computers
  • Usually refers to X-ray CT
  • Positron (PET)
  • Gamma rays (SPECT)

5
Cross-Sections by X-Ray Projections
  • Project X-ray through biological tissuemeasure
    total absorption of ray by tissue
  • Projection P?(t) is the Radontransform of object
    functionf(x,y)
  • Total set of projections calledsinogram

6
X-Ray Projection Example
7
Phantom and Sinogram
Shepp-Logan Phantom
8
CT Reconstruction
  • Restore image from projection data
  • Inverse Radon transform
  • Most common algorithm is filtered backprojection
  • Smear each projection over image plane

9
Fourier Slice Theorem
  • Fourier transform of a 2-D object projected onto
    a line is equal to a slice of a 2-D Fourier
    transform of the object
  • Allows image reconstruction from projection data
  • Overlay FT of projections in 2-D Fourier domain
  • If carried out in space domain, becomes
    backprojection procedure

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Backprojection Result
  • Need filtering (high-pass), interpolation

20
FBP Algorithm
  • Input sinogram sino(?, n)
  • Output image img(x,y)
  • for each ?
  • filter sino(?,)
  • for each x
  • for each y
  • n x cos ? y sin ?
  • img(x,y) sino(?, n) img(x,y)
  • O(n3) algorithm
  • But highly parallelizable, given sufficient
    memory bandwidth not computationally intensive

21
  • Single-Slice Rebinning Methodfor Helical
    Cone-Beam CT

22
3-D Tomography
  • Construct 3-D image using sequence ofcross
    sectional images
  • Requires many passes of ionizing x-ray radiation

23
Helical Cone-Beam Scanner
  • Helical traversal reduces total number of passes
    increases scanning speed and reduces x-ray
    exposure
  • However, need to convertcone-beam data into
    stackof fan-beam slice images

24
Rebinning
  • Maps projection data into fan-beam slices
  • Virtual fan source mapped to surface of cone
    source
  • Each slice requires CB projections from 1
    revolution centered on that slice (/- 0.5P)

25
Rebinning
  • Fan-beam projection estimated from value of
    cone-beam projection in same vertical plane
  • Use closest cone-beam source directly above or
    below virtual fan-beam source
  • Use oblique ray passing through M

26
Rebinning Geometry
27
Rebinning Equation
  • Each fan-beam value is just weighted version of
    cone-beam projection data

fan-beam projection length
fan sino
CB sino
cone-beam projection length
28
Simulation Comparisons
  • A Single detector row (no oblique rays), 5mm
    pitch CSH-HS algorithm
  • B Seven detector rows, 25mm pitch CB-SSRB
    algorithm
  • C Seven detector rows, 100mm pitch Full 3-D
    backprojection algorithm
  • D Seven detector rows, 100mm pitch CB-SSRB
    algorithm

29
Simulation Comparisons
30
Simulation Comparisons
31
Performance Comparison
  • Runtime for (C) 276s CPU, using 27 ray-sums
  • Runtime for (D) 1310s CPU, using 57 ray-sum
  • Runtimes for (A) and (B) about equal

32
Conclusions
  • Like all CT, CB-SSRB is not exact reconstruction
    artifacts can affect image quality
  • However, good performance for large-pitch helixes
  • 5x larger pitch 5x fewer projection
    measurements
  • Selection of oblique rays integral to performance
  • Need multiple detector rows (7 vs. 1)

33
References
  • http//en.wikipedia.org/wiki/Tomography
  • http//en.wikipedia.org/wiki/Computed_tomography
  • Kak, A. C., Slaney, M., Principles of
    Computerized Tomographic Imaging, IEEE Press, 1988
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