  This project is aimed at designing the fast forward projection algorithm and
also the backprojection algorithm for cone beam CT imaging systems with
circular X-ray source trajectory. The principle of the designs is based on
utilizing the potential computational efficiency which the Fourier Slice
Theorem and the Non-uniform Fast Fourier Transform (NUFFT) will bring forth. In
this Masters report, the detailed design of the NUFFT based forward projector
including a novel 3D (derivative of) Radon space resampling method will be
given. Meanwhile the complexity of the NUFFT based forward projector is
analysed and compared with the non-Fourier based CT projector, and the
advantage of the NUFFT based forward projection in terms of the computational
efficiency is demonstrated in this report. Base on the design of the forward
algorithm, the NUFFT based 3D direct reconstruction algorithm will be derived.
The experiments will be taken to test the performance of the forward algorithm
and the backprojection algorithm to show the practicability and accuracy of
these designs by comparing them jointly with the well-acknowledged cone beam CT
operators: the CT linear interpolation forward projector and the FDK algorithm.
This Master report will demonstrate a novel and efficient way of implementing
the cone beam CT operator, a detailed summary of the project, and the future
research prospects of the NUFFT based cone beam CT algorithms.
