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The cone‐beam algorithm of Feldkamp, Davis, and Kress preserves oblique line integrals
Author(s) -
Rodet Thomas,
Noo Frédéric,
Defrise Michel
Publication year - 2004
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 - 10.1118/1.1759828
Subject(s) - oblique case , line integral , line (geometry) , cone (formal languages) , mathematics , orbit (dynamics) , reconstruction algorithm , beam (structure) , invariant (physics) , iterative reconstruction , algorithm , cone beam computed tomography , geometry , optics , physics , mathematical analysis , computer vision , computer science , integral equation , computed tomography , medicine , radiology , engineering , philosophy , linguistics , aerospace engineering , mathematical physics
The algorithm of Feldkamp, Davis, and Kress [J. Opt. Soc. Am. A 1 , 612–619 (1984)] is a widely used filtered‐backprojection algorithm for three‐dimensional image reconstruction from cone‐beam (CB) projections measured with a circular orbit of the x‐ray source. A well‐known property of this approximate algorithm is that the integral of the reconstructed image along any axial line orthogonal to the plane of the orbit is exact when the cone‐beam projections are not truncated. We generalize this result to oblique line integrals, thus providing an efficient method to compute synthetic radiographs from cone‐beam projections. Our generalized result is obtained by showing that the FDK algorithm is invariant under transformations that map oblique lines onto axial lines.