用于偏置的扇形探头的Fourier域图像重建

For parallel beam geometry the Fourier reconstruction works via the central slice theorem. For fan beam geometry the central slice theorem in its simple form does not exist. But a generalized central slice theorem for fan beam geometry has been introduced for fan beam geometry by the author of this paper. This method fills the frequency plane by adding up the contributions from all projections. Fast Fourier transform is done afterwards to get the space-domain image. One of the advantage of this method over the filtered back-projection method is that it can offer a exact image reconstruction in case of the short scan, i.e. the x-ray source only rotated the object 180 degree plus the span angle of the fan beam. An additional advantage is that the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the frequency domain. This paper extents this method to the reconstruction for the offsetted detector. Here offsetted detector means that the detector line is shift to one side. Offsetted detector is often used to extent the detector line. Since short detector line often causes the measured projections are truncated which in turn results severe truncation artifacts on the reconstructed image. It is dificult to get a exact results for the offsetted fan beam reconstruction using the filtered back-projection method. Rebinning technique can obtained parallel beam projections from fan-beam projection and hence can offer a exact reconstruction. But derect rebinning from fan-beam to parallel beam often means an aditional interpolation which increases the artifacts too. In this paper we extent this method and show that in the case of the offsetted detector the fan-beam Fourier-domain reconstruction can offer a exact results and does not introduce more interpolations.