Inverse Fourier Transform in the Gamma Coordinate System
Joint Authors
Wei, Yuchuan
Yu, Hengyong
Wang, G.
Source
International Journal of Biomedical Imaging
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-10-26
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
This paper provides auxiliary results for our general scheme of computed tomography.
In 3D parallel-beam geometry, we first demonstrate that the inverse Fourier transform in different coordinate systems leads to different reconstruction formulas and explain why the Radon formula cannot directly work with truncated projection data.
Also, we introduce a gamma coordinate system, analyze its properties, compute the Jacobian of the coordinate transform, and define weight functions for the inverse Fourier transform assuming a simple scanning model.
Then, we generate Orlov's theorem and a weighted Radon formula from the inverse Fourier transform in the new system.
Furthermore, we present the motion equation of the frequency plane and the conditions for sharp points of the instantaneous rotation axis.
Our analysis on the motion of the frequency plane is related to the Frenet-Serret theorem in the differential geometry.
American Psychological Association (APA)
Wei, Yuchuan& Yu, Hengyong& Wang, G.. 2010. Inverse Fourier Transform in the Gamma Coordinate System. International Journal of Biomedical Imaging،Vol. 2011, no. 2011, pp.1-16.
https://search.emarefa.net/detail/BIM-460343
Modern Language Association (MLA)
Wei, Yuchuan…[et al.]. Inverse Fourier Transform in the Gamma Coordinate System. International Journal of Biomedical Imaging No. 2011 (2011), pp.1-16.
https://search.emarefa.net/detail/BIM-460343
American Medical Association (AMA)
Wei, Yuchuan& Yu, Hengyong& Wang, G.. Inverse Fourier Transform in the Gamma Coordinate System. International Journal of Biomedical Imaging. 2010. Vol. 2011, no. 2011, pp.1-16.
https://search.emarefa.net/detail/BIM-460343
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-460343