Literature%20Review

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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
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Background

• Computed Tomography

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Tomography

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

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Computed Tomography (CT)

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

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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

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X-Ray Projection Example
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Phantom and Sinogram
Shepp-Logan Phantom
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CT Reconstruction

• Restore image from projection data
• Inverse Radon transform
• Most common algorithm is filtered backprojection
• Smear each projection over image plane

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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

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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

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• Single-Slice Rebinning Methodfor Helical
  Cone-Beam CT

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3-D Tomography

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

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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

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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)

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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

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Rebinning Geometry
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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
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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

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Simulation Comparisons
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Simulation Comparisons
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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

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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)

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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