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Applied Optics

Applied 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)

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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

Original Manuscript: April 29, 2003
Revised Manuscript: August 20, 2003
Published: December 10, 2003

Zikuan Chen and Ruola Ning, "Filling the Radon domain in computed tomography by local convex combination," Appl. Opt. 42, 7043-7051 (2003)

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  1. G. Besson, “CT image reconstruction from fan-parallel data,” Med. Phys. 26, 415–426 (1999). [CrossRef]
  2. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1987).
  3. I. Svalbe, D. Spek, “Reconstruction of tomographic images using analog projections and the digital Radon transform,” Linear Algebr. Appl. 339, 125–145 (2001). [CrossRef]
  4. X. Pan, “Optimal noise control in and fast reconstruction of fanbeam computed tomography imaging,” Med. Phys. 26, 289–297 (1999). [CrossRef]
  5. I. Amidror, “Scattered data interpolation methods for electronic imaging systems: a survey,” J. Electron. Imaging 11, 157–176 (2002). [CrossRef]
  6. S. E. Parker, “Nearest-grid-point interpolation in gyrokinetic particle-in-cell simulation,” J. Comput. Phys. 178, 520–532 (2002). [CrossRef]
  7. D. Rajan, S. Chaudhuri, “Generalized interpolation and its application in super-resolution imaging,” Image Vision Comput. 19, 957–969 (2001). [CrossRef]
  8. W. K. Carey, D. B. Chuang, S. S. Hemami, “Regularity-preserving image interpolation,” IEEE Trans. Image Proc. 8, 1293–1297 (1999). [CrossRef]
  9. J. A. Parker, R. V. Kenyon, D. E. Troxel, “Comparison of interpolating methods for image resampling,” IEEE Trans. Med. Imaging 2, 31–39 (1983). [CrossRef] [PubMed]
  10. G. R. Davis, “Faster tomographic fanbeam back-projection using Cartesian axes pre-projection,” Nucl. Instrum. Methods Phys. Res. A 410, 329–334 (1998). [CrossRef]
  11. F. Noo, M. Defrise, R. Clackdoyle, H. Kudo, “Image reconstruction from fanbeam projections on less than a short scan,” Phys. Med. Biol. 47, 2525–2546 (2002). [CrossRef] [PubMed]
  12. H. W. Guggenheimer, Applicable Geometry: Global and Local Convexity, (Krieger, New York, 1977).
  13. S. Bonnet, F. Peyrin, F. Turjman, R. Prost, “Multiresolution reconstruction in fanbeam tomography,” IEEE Trans. Image Proc. 11, 169–176 (2002). [CrossRef]
  14. Z. Chen, R. Ning, “Why should breast tumour detection go three dimensional?” Phys. Med. Biol. 48, 2217–2228 (2003). [CrossRef] [PubMed]

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