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CT Reconstruction
 
  Introduction Description roundleft Animation roundright Example  

   
bullet Radon Transform
  Let tex2html_wrap_inline308 be an image. The Radon transform operator tex2html_wrap_inline310 is defined as follows:
equation69
where tex2html_wrap_inline312 is the Dirac impulse and tex2html_wrap_inline314 is the unit vector specifying the direction of the integration. The function tex2html_wrap_inline316 is sometimes called a parallel projection.
   
bullet Radon Transform of a B-spline
 
 equation203

Spline flower

   
bullet The Fourier Slice theorem
  The Fourier Slice Theorem states the equivalence between the one-dimensional Fourier transform of a parallel projection and a slice in the two-dimensional Fourier transform of an image.
 equation82
bullet Filtered Backprojection
  A reconstruction formula for tex2html_wrap_inline320 is given by:
equation89
where
equation97
with tex2html_wrap_inline322.
  The animation shows the reconstruction process for the Shepp-Logan phantom and the CT-slice.
Shepp-Logan: QuickTime format or MPEG format.
Ct-slice: QuickTime format or MPEG format.

EPFL Swiss Federal Institute of Technology Lausanne
BIG Biomedical Imaging Group
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Imaging Web Demonstration
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23 February 2000