A unified framework for exact cone-beam reconstruction formulas.
In this paper, we present concise proofs of several recently developed exact cone-beam reconstruction methods in the Tuy inversion framework, including both filtered-backprojection and backprojection-filtration formulas in the cases of standard spiral, nonstandard spiral, and more general scanning loci. While a similar proof of the Katsevich formula was previously reported, we present a new proof of the Zou and Pan backprojection-filtration formula. Our proof combines both odd and even data extensions so that only the cone-beam transform itself is utilized in the backprojection-filtration inversion. More importantly, our formulation is valid for general smooth scanning curves, in agreement with an earlier paper from our group [Ye, Zhao, Yu, and Wang, Proc. SPIE 5535, 293-300 (Aug. 6 2004)]. As a consequence of that proof, we obtain a new inversion formula, which is in a two-dimensional filtering backprojection format. A possibility for generalization of the Katsevich filtered-backprojection reconstruction method is also discussed from the viewpoint of this framework.
Zhao
Shiying
S
CT/Micro-CT Laboratory, Department of Radiology, University of Iowa, 200 Hawkins Drive, Iowa City, Iowa 52242, USA. shiying-zhao@uiowa.edu
Yu
Hengyong
H
Wang
Ge
G
D000465:Algorithms; D021621:Imaging, Three-Dimensional; D015233:Models, Statistical; D010363:Pattern Recognition, Automated; D019047:Phantoms, Imaging; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D012680:Sensitivity and Specificity; D012984:Software; D013382:Subtraction Technique; D036542:Tomography, Spiral Computed / Q000379:methods*; D014057:Tomography, X-Ray Computed / Q000379:methods*