Expressions for the fan beam and parallel beam projection and back-projection operators are given along with an evaluation of the point source response for the back-projection operators. The back-projection operator for the fan beam geometry requires the superposition of projection data measured over 360°. Both the fan beam and parallel beam geometries have back-projection operators with point source responses which are proportional to l/|r-r0| and thus two-dimensional Fourier filter techniques can be used to reconstruct transverse sections from fan beam and parallel beam projection data. The two-dimensional Fourier filter techniques may have the speed over other methods for reconstructing fan beam data but the reconstructed image requires four times the core storage so that the convolution result of one period does not overlap the convolution result of the succeeding period when implementing the fast Fourier transform.
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