Add to BibSonomyAbstract
Radon data interpolation is a necessary procedure in computed tomography (CT), especially for reconstruction from divergent beam scanning. In a polar-grid representation, the Radon data of a fanbeam projection are populated on an arc, rather on a radial line. Collectively, the Radon data generated from a fanbeam CT system are unevenly populated: The population becomes sparser as the polar distance increases. In CT reconstruction, the Fourier central slice theorem requires a radial scanline full of Radon data. Therefore the vacant entries of a scanline must be filled by interpolation. In addition, interpolation is also required in polar-to-Cartesian conversion. In this paper we propose a practical interpolation technique for filling the vacant entries by local convex combination. It is a linear interpolant that generates a value for a grid point from the available data lying in its neighborhood, by a weighted average, with the weights corresponding to the inverse distances. In fact, the linear convex combination serves as a general flat-smoothing operation in filling a vacancy. Specifically, this technique realizes a variety of linear interpolations, including nearest-neighbor replication, two-point collinear, three-point triangulation, and four-point quadrilateral, and local extrapolation, in a unified framework. Algorithms and a simulation demonstration are provided.
© 2003 Optical Society of America
Full Article | PDF ArticleMore Like This
Kenneth M. Hanson and George W. Wecksung
Appl. Opt. 24(23) 4028-4039 (1985)
Adam M. Zysk, J. Josh Reynolds, Daniel L. Marks, P. Scott Carney, and Stephen A. Boppart
Opt. Lett. 28(9) 701-703 (2003)
Hiroyuki Kudo and Tsuneo Saito
J. Opt. Soc. Am. A 8(7) 1148-1160 (1991)