Article
X-Ray Transform and 3D Radon Transform for Ellipsoids and Tetrahedra
Journal of X-Ray Science and Technology
(2004)
Abstract
Accurate simulation of X-ray transforms of representative objects plays an important role in the evaluation and improvement of CT reconstruction algorithms. In this paper, we formulate the X-ray transform and 3D Radon transform for ellipsoids and tetrahedra, and verify the resulting formulas by numerical simulation. Here the ellipsoids and tetrahedra may be arbitrarily positioned and rotated. Linearity of the first derivative of radon transform is observed. Our results serve as a benchmark for development of various cone-beam algorithms that work through the Radon space, such as Grangeat-type algorithms.
Keywords
- Computed tomography,
- Cone-beam geometry,
- X-ray transform,
- 3D Radon transform,
- Grangeat formula,
- Shepp-Logan phantom
Disciplines
Publication Date
2004
Citation Information
Jiehua Zhu, Seung Wook Lee, Yangbo Ye, Shiying Zhao, et al.. "X-Ray Transform and 3D Radon Transform for Ellipsoids and Tetrahedra" Journal of X-Ray Science and Technology Vol. 12 Iss. 4 (2004) p. 215 - 229 ISSN: 1095-9114 Available at: http://works.bepress.com/jiehua_zhu/43/