Derivation and implementation of a cone-beam reconstruction algorithm for nonplanar orbits

Journal Article · Tue Mar 01 00:00:00 EST 1994 · IEEE Transactions on Medical Imaging (Institute of Electrical and Electronics Engineers); (United States)

DOI:https://doi.org/10.1109/42.276158· OSTI ID:7144731

Kudo, Hiroyuki; Saito, Tsuneo ^[1]

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1. Univ. of Tsukuba (Japan). Inst. of Information Sciences and Electronics

Smith and Grangeat derived a cone-beam inversion formula that can be applied when a nonplanar orbit satisfying the completeness condition is used. Although Grangeat's inversion formula is mathematically different from Smith's, they have similar overall structures to each other. The contribution of this paper is two-fold. First, based on the derivation of Smith, the authors point out that Grangeat's inversion formula and Smith's can be conveniently described using a single formula (the Smith-Grangeat inversion formula) that is in the form of space-variant filtering followed by cone-beam backprojection. Furthermore, the resulting formula is reformulated for data acquisition systems with a planar detector to obtain a new reconstruction algorithm. Second, the authors make two significant modifications to the new algorithm to reduce artifacts and numerical errors encountered in direct implementation of the new algorithm. As for exactness of the new algorithm, the following fact can be stated. The algorithm based on Grangeat's intermediate function is exact for any complete orbit, whereas that based on Smith's intermediate function should be considered as an approximate inverse excepting the special case where almost every plane in 3-D space meets the orbit. The validity of the new algorithm is demonstrated by simulation studies.

• OSTI ID: 7144731
• Journal Information: IEEE Transactions on Medical Imaging (Institute of Electrical and Electronics Engineers); (United States), Vol. 13:1; ISSN 0278-0062
• Country of Publication: United States
• Language: English

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