## Practical cone-beam algorithm

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

http://dx.doi.org/10.1364/JOSAA.1.000612

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### Abstract

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

**History**

Original Manuscript: November 11, 1983

Manuscript Accepted: February 28, 1984

Published: June 1, 1984

**Citation**

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

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-1-6-612

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### References

- See, for example, references contained in G. T. Herman, Image Reconstruction from Projections (Academic, New York, 1980), Chap. 14.
- R. A. Robb, A. H. Lent, B. K. Gilbert, A. Chu, “The dynamic spatial reconstructor,”J. Med. Syst. 4, 253–288 (1980). [CrossRef]
- 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).
- J. G. Colsher, “Iterative three-dimensional image reconstruction, from tomographic projections,” Comput. Graphics Image Processing, 6, 513–537 (1977). [CrossRef]
- 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.
- 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).
- M. Schlindwein, “Iterative three-dimensional reconstruction from twin-cone beam projections,”IEEE Trans. Nucl. Sci. NS-25, 1135–1143 (1978). [CrossRef]
- G. Kowalski, “Multislice reconstruction from twin-cone beam scanning,”IEEE Trans. Nucl. Sci. NS-26, 2895–2903 (1979). [CrossRef]
- 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]
- O. Nalcioglu, Z. H. Cho, “Reconstruction of 3-d objects from cone-beam projections,” Proc. IEEE 66, 1584–1585 (1978). [CrossRef]
- 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]
- H. K. Tuy, “An inversion formula for cone-beam reconstruction,” (State University of New York at Buffalo, Buffalo, N.Y., June, 1981).
- G. N. Minerbo, “Convolutional Reconstruction from cone-beam projection data,”IEEE Trans. Nucl. Sci. NS-26, 2682–2684 (1979). [CrossRef]
- 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).
- G. T. Herman, A. V. Lakshminarayanan, A. Naparstek, “Convolution reconstruction techniques for divergent beams,” Comput. Biol. Med. 6, 259–271 (1976). [CrossRef] [PubMed]
- 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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