Filling the Radon domain in computed tomography by local convex combination.
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.
Chen
Zikuan
Z
Department of Radiology, University of Rochester, Box 648, 601 Elmwood Avenue, Rochester, New York 14642, USA. zikuan_chen@urmc.rochester.edu
Ning
Ruola
R
D000465:Algorithms; D003198:Computer Simulation; D005583:Fourier Analysis; D008962:Models, Theoretical; D011886:Radon; D014057:Tomography, X-Ray Computed
D011886:Radon