Premium
A unified framework for exact cone‐beam reconstruction formulas
Author(s) -
Zhao Shiying,
Yu Hengyong,
Wang Ge
Publication year - 2005
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.1869632
Subject(s) - mathematical proof , iterative reconstruction , generalization , mathematics , inversion (geology) , algorithm , calculus (dental) , mathematical analysis , geometry , computer science , artificial intelligence , medicine , paleontology , dentistry , structural basin , biology
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.