The Non-uniform Fast Fourier Transform in Computed Tomography

TL;DR

This paper introduces a novel NUFFT-based algorithm for cone beam CT imaging that enhances computational efficiency in forward projection and backprojection, with detailed design, analysis, and experimental validation.

Contribution

It presents the first detailed design of NUFFT-based 3D forward and backprojection algorithms for cone beam CT, demonstrating improved efficiency over traditional methods.

Findings

NUFFT-based forward projector is more computationally efficient.

The algorithms show comparable accuracy to existing CT operators.

Experimental results validate the practicality of the proposed methods.

Abstract

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.