Journal article
X-ray transform and 3D Radon transform for ellipsoids and tetrahedra
Journal of X-ray science and technology, Vol.12(4), pp.215-229
01/01/2004
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.
Details
- Title: Subtitle
- X-ray transform and 3D Radon transform for ellipsoids and tetrahedra
- Creators
- Jiehua Zhu - Univ Iowa, Dept Math, Iowa City, IA 52242 USASeung Wook Lee - Korea Atom Energy Res Inst, Taejon 305600, South KoreaYangbo Ye - Univ Iowa, Dept Math, Iowa City, IA 52242 USAShiying Zhao - Univ Iowa, Dept Radiol, Iowa City, IA 52242 USAGe Wang - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Journal of X-ray science and technology, Vol.12(4), pp.215-229
- Publisher
- IOS PRESS
- ISSN
- 0895-3996
- eISSN
- 1095-9114
- Number of pages
- 15
- Grant note
- R01 DC03590 / NIH
- Language
- English
- Date published
- 01/01/2004
- Academic Unit
- Mathematics
- Record Identifier
- 9984240869102771
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