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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 42, Iss. 35 — Dec. 10, 2003
  • pp: 7043–7051

Filling the Radon Domain in Computed Tomography by Local Convex Combination

Zikuan Chen and Ruola Ning  »View Author Affiliations


Applied Optics, Vol. 42, Issue 35, pp. 7043-7051 (2003)
http://dx.doi.org/10.1364/AO.42.007043


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Abstract

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

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(110.6960) Imaging systems : Tomography
(340.7440) X-ray optics : X-ray imaging

Citation
Zikuan Chen and Ruola Ning, "Filling the Radon Domain in Computed Tomography by Local Convex Combination," Appl. Opt. 42, 7043-7051 (2003)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-42-35-7043

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