Inverse Fourier Transform in the Gamma Coordinate SystemReportar como inadecuado




Inverse Fourier Transform in the Gamma Coordinate System - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

International Journal of Biomedical ImagingVolume 2011 2011, Article ID 285130, 16 pages

Research Article

Department of Radiation Oncology, Wake Forest University School of Medicine, Winston-Salem, NC 27157, USA

Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Sciences, Wake Forest University Health Sciences, Winston-Salem, NC 27157, USA

Department of Radiology, Division of Radiologic Sciences, Wake Forest University Health Sciences, Winston-Salem, NC 27157, USA

Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Sciences, Virginia Tech., Blacksburg, VA 24061, USA

Received 28 May 2010; Accepted 29 July 2010

Academic Editor: Yangbo Ye

Copyright © 2011 Yuchuan Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.





Autor: Yuchuan Wei, Hengyong Yu, and Ge Wang

Fuente: https://www.hindawi.com/



DESCARGAR PDF




Documentos relacionados