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Filtered backprojection formula for exact image reconstruction from cone‐beam data along a general scanning curve
Author(s) -
Ye Yangbo,
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 - 10.1118/1.1828673
Subject(s) - chord (peer to peer) , mathematics , iterative reconstruction , cone (formal languages) , generalization , geometry , mathematical analysis , algorithm , artificial intelligence , computer science , distributed computing
Recently, Katsevich proved a filtered backprojection formula for exact image reconstruction from cone‐beam data along a helical scanning locus, which is an important breakthrough since 1991 when the spiral cone‐beam scanning mode was proposed. In this paper, we prove a generalized Katsevich's formula for exact image reconstruction from cone‐beam data collected along a rather flexible curve. We will also give a general condition on filtering directions. Based on this condition, we suggest a natural choice of filtering directions, which is more convenient than Katsevich's choice and can be applied to general scanning curves. In the derivation, we use analytical techniques instead of geometric arguments. As a result, we do not need the uniqueness of the PI lines. In fact, our formula can be used to reconstruct images on any chord as long as a scanning curve runs from one endpoint of the chord to the other endpoint. This can be considered as a generalization of Orlov's classical theorem. Specifically, our formula can be applied to (i) nonstandard spirals of variable radii and pitches (with PI‐ or n ‐PI‐windows), and (ii) saddlelike curves.