Scheme of computed tomography

Article type: Research Article

Authors: Wei, Yuchuan | Yu, Hengyong | Hsieh, Jiang | Cong, Wenxiang | Wang, Ge^;

Affiliations: Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Science, Wake Forest University, Winston-Salem, NC 27157, USA | Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Science, Virginia Tech, Blacksburg, VA 24061, USA | Laboratories of Applied Science, GE Healthcare Technologies, Milwaukee, WI 53201, USA

Note: [] Corresponding authors. E-mail: [email protected]; [email protected]

Abstract: Since Katsevich's work on cone-beam CT in 2002, a series of new reconstruction formulae for cone-beam and fan-beam reconstruction have been published. To understand these new results in a unified way, two schemes were proposed in the literature: one is based on the Radon formula, while the other on the Tuy formula. In the paper, we present a general two-step scheme for parallel-, fan- and cone-beam CT based on the inverse Fourier transform. We first derive parallel-beam formulae and then translate them to the divergent-beam case via a standardized method. This complete framework not only provides a single mechanism for the deduction of most existing CT formulae but also generates new algorithms. Meanwhile, along the development of this new framework some minor flaws are identified and fixed in publications. Additionally, the traditional assumption that an object be compactly supported inside a scanning trajectory is no longer needed.

Keywords: Computed Tomography (CT), Fourier analysis, convolution theorem, Dirac function, two-step scheme, instantaneous cylindrical system, three-step method, weighted back-projection (WBP), weighted Hilbert transform (WHT), frequency plane, dartboard function, Outward-homeward function, J function, odd/even extension, cone-beam, complete region, trajectory projection

Journal: Journal of X-Ray Science and Technology, vol. 15, no. 4, pp. 235-270, 2007