One of the drawbacks of the Fourier reconstruction-based approach is the lack of good, efficient interpolation schemes to convert from the polar grid to the Cartesian grid that are needed to do the inverse FFT. Siemens Computerized Tomography group has developed an interpolation scheme that addresses such a shortcoming. In this article we present a parallel approach for a Fourier reconstruction-based method that uses this interpolation scheme. We also present a parallel approach of the rebinning method used with the approach. The rebinning method is used to convert the acquired fan projections into parallel projections. We give an overview of the method, provide the mapping approach proposed to parallelize the algorithms, present a brief description of the architecture used in the simulation, describe the simulation model, and give the simulation results.