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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 1, Iss. 6 — Jun. 1, 1984
  • pp: 612–619

Practical cone-beam algorithm

L. A. Feldkamp, L. C. Davis, and J. W. Kress  »View Author Affiliations

JOSA A, Vol. 1, Issue 6, pp. 612-619 (1984)

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A convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections. The formula is approximate but has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation. It reduces to the standard fan-beam formula in the plane that is perpendicular to the axis of rotation and contains the point source. The algorithm is applied to a mathematical phantom as an example of its performance.

© 1984 Optical Society of America

Original Manuscript: November 11, 1983
Manuscript Accepted: February 28, 1984
Published: June 1, 1984

L. A. Feldkamp, L. C. Davis, and J. W. Kress, "Practical cone-beam algorithm," J. Opt. Soc. Am. A 1, 612-619 (1984)

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  1. See, for example, references contained in G. T. Herman, Image Reconstruction from Projections (Academic, New York, 1980), Chap. 14.
  2. R. A. Robb, A. H. Lent, B. K. Gilbert, A. Chu, “The dynamic spatial reconstructor,”J. Med. Syst. 4, 253–288 (1980). [CrossRef]
  3. M. D. Alschuler, Y. Censor, G. T. Herman, A. Lent, R. M. Lewitt, S. N. Srihari, H. Tuy, J. K. Udupa, “Mathematical aspects of image reconstruction from projections,” (State University of New York at Buffalo, Buffalo, N.Y., May, 1981).
  4. J. G. Colsher, “Iterative three-dimensional image reconstruction, from tomographic projections,” Comput. Graphics Image Processing, 6, 513–537 (1977). [CrossRef]
  5. M. D. Altschuler, G. T. Herman, A. Lent, “Fully three dimensional reconstruction from cone-beam sources,” in Proceedings of the Conference on Pattern Recognition and Image Processing (IEEE Computer Society, Long Beach, Calif., 1978), pp. 194–199.
  6. M. D. Altschuler, Y. Censor, P. P. B. Eggermont, G. T. Herman, Y. H. Kuo, R. M. Lewitt, M. McKay, H. Tuy, J. Udupa, M. M. Yau, “Demonstration of a software package for the reconstruction of the dynamically changing structure of the human heart from cone-beam x-ray projections,” (State University of New York at Buffalo, Buffalo, N.Y., August, 1979).
  7. M. Schlindwein, “Iterative three-dimensional reconstruction from twin-cone beam projections,”IEEE Trans. Nucl. Sci. NS-25, 1135–1143 (1978). [CrossRef]
  8. G. Kowalski, “Multislice reconstruction from twin-cone beam scanning,”IEEE Trans. Nucl. Sci. NS-26, 2895–2903 (1979). [CrossRef]
  9. H. E. Knutsson, P. Edholm, G. H. Granlund, C. Petersson, “Ectomography—a new radiographic reconstruction method, I., II.,”IEEE Trans. Biomed. Eng. BME-27, 640–655 (1980). [CrossRef]
  10. O. Nalcioglu, Z. H. Cho, “Reconstruction of 3-d objects from cone-beam projections,” Proc. IEEE 66, 1584–1585 (1978). [CrossRef]
  11. R. V. Denton, B. Friedlander, A. J. Rockmore, “Direct three-dimensional image reconstruction from divergent rays,”IEEE Trans. Nucl. Sci. NS-26, 4695–4703 (1979). [CrossRef]
  12. H. K. Tuy, “An inversion formula for cone-beam reconstruction,” (State University of New York at Buffalo, Buffalo, N.Y., June, 1981).
  13. G. N. Minerbo, “Convolutional Reconstruction from cone-beam projection data,”IEEE Trans. Nucl. Sci. NS-26, 2682–2684 (1979). [CrossRef]
  14. R. M. Lewitt, M. R. McKay, “Description of a software package for computing cone-beam x-ray projections of time-varying structures, and for dynamic three-dimensional image reconstruction,” (State University of New York at Buffalo, Buffalo, N.Y., May, 1980).
  15. G. T. Herman, A. V. Lakshminarayanan, A. Naparstek, “Convolution reconstruction techniques for divergent beams,” Comput. Biol. Med. 6, 259–271 (1976). [CrossRef] [PubMed]
  16. L. A. Shepp, B. F. Logan, “The Fourier reconstruction of a head section,”IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974).

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