26 October 2004 Exact reconstruction for cone-beam scanning along nonstandard spirals and other curves
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In this article we consider cone-beam CT projections along a nonstandard 3-D spiral with variable radius and variable pitch. Specifically, we generalize an exact image reconstruction formula by Zou and Pan (2004a) and (2004b) to the case of nonstandard spirals, by giving a new, analytic proof of the reconstruction formula. Our proof is independent of the shape of the spiral, as long as the object is contained in a region inside the spiral, where there is a PI line passing through any interior point. Our generalized reconstruction formula can also be applied to much more general situations, including cone-beam scanning along standard (Pack, et al. 2004) and nonstandard saddle curves, and any smooth curve from one endpoint of a line segment to the other endpoint, for image reconstruction of that line segment. In other words, our results can be regarded as a generalization of Orlov's classical papers (1975) to cone-beam scanning.
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Yangbo Ye, Shiying Zhao, Hengyong Yu, Ge Wang, "Exact reconstruction for cone-beam scanning along nonstandard spirals and other curves", Proc. SPIE 5535, Developments in X-Ray Tomography IV, (26 October 2004); doi: 10.1117/12.559087; https://doi.org/10.1117/12.559087

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