Novel Properties Of The Fourier Decomposition Of The Sinogram

Paul R. Edholm; Robert M. Lewitt; Bernt Lindholm

doi:10.1117/12.966672

1 January 1986 Novel Properties Of The Fourier Decomposition Of The Sinogram

Paul R. Edholm, Robert M. Lewitt, Bernt Lindholm

Proceedings Volume 0671, Physics and Engineering of Computerized Multidimensional Imaging and Processing; (1986) https://doi.org/10.1117/12.966672
Event: Physics and Engineering of Computerized Multidimensional Imaging and Processing, 1986, Newport Beach, CA, United States

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.

Citation Download 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, (1 January 1986); https://doi.org/10.1117/12.966672

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