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Proceedings Article

Novel Properties Of The Fourier Decomposition Of The Sinogram

[+] Author Affiliations
Paul R. Edholm, Robert M. Lewitt

University of Pennsylvania (United States)

Bernt Lindholm

University of Linkoping (Sweden)

Proc. SPIE 0671, Physics and Engineering of Computerized Multidimensional Imaging and Processing, 8 (January 1, 1986); doi:10.1117/12.966672
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From Conference Volume 0671

  • Physics and Engineering of Computerized Multidimensional Imaging and Processing
  • Thomas F. Budinger; Zang-Hee Cho; Orhan Nalcioglu
  • Newport Beach, United States | April 02, 1988

abstract

The double Fourier decomposition of the sinogram is obtained by first taking the Fourier transform of each parallel-ray projection and then calculating the coefficients of a Fourier series with respect to angle for each frequency component of the transformed projections. The values of these coefficients may be plotted on a two-dimensional map whose coordinates are spatial frequency w (continuous) and angular harmonic number n (discrete). For |w| large, the Fourier coefficients on the line n=kw of slope k through the origin of the coefficient space are found to depend strongly on the contributions to the projection data that, for each view, come from a certain distance to the detector plane, where the distance is a linear function of k. The values of these coefficients depend only weakly on contributions from other distances from the detector. The theoretical basis of this property is presented in this paper and a potential application to emission computerized tomography is discussed.

© (1986) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Citation

Paul R. Edholm ; Robert M. Lewitt and Bernt Lindholm
"Novel Properties Of The Fourier Decomposition Of The Sinogram", Proc. SPIE 0671, Physics and Engineering of Computerized Multidimensional Imaging and Processing, 8 (January 1, 1986); doi:10.1117/12.966672; http://dx.doi.org/10.1117/12.966672


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