Videographic tomography. I. Reconstruction with parallel-beam projection data

1990 ◽  
Vol 9 (4) ◽  
pp. 366-375 ◽  
Author(s):  
A.F. Gmitro ◽  
V. Tresp ◽  
G.R. Gindi
Keyword(s):  
Projection Data ◽  
Parallel Beam ◽  
Beam Projection

scholarly journals Data correlation based noise level estimation for cone beam projection data

2017 ◽  
Vol 25 (6) ◽  
pp. 907-926 ◽  
Author(s):  
Ti Bai ◽  
Hao Yan ◽  
Luo Ouyang ◽  
David Staub ◽  
Jing Wang ◽  
...  
Keyword(s):  
Noise Level ◽  
Cone Beam ◽  
Projection Data ◽  
Data Correlation ◽  
Noise Level Estimation ◽  
Beam Projection

scholarly journals Inverse Fourier Transform in the Gamma Coordinate System

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Yuchuan Wei ◽  
Hengyong Yu ◽  
Ge Wang
Keyword(s):  
Fourier Transform ◽  
Coordinate System ◽  
Inverse Fourier Transform ◽  
Rotation Axis ◽  
General Scheme ◽  
Weight Functions ◽  
Projection Data ◽  
Parallel Beam ◽  
Beam Geometry ◽  
Parallel Beam Geometry

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.

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