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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 5, Iss. 3 — Mar. 1, 1988
  • pp: 331–343

Shape estimation in computer tomography from minimal data

Henry Stark and Hui Peng  »View Author Affiliations


JOSA A, Vol. 5, Issue 3, pp. 331-343 (1988)
http://dx.doi.org/10.1364/JOSAA.5.000331


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Abstract

In computerized tomography, line integrals of the absorptivity are used to reconstruct the object. In some applications only the locations, sizes, and shapes of internal opacities or near-opacities are needed. For these applications it is unnecessary to reconstruct an image by convolution backprojection [O(N3)] or by direct Fourier methods [O(N2 log N)]. We propose an algorithm suitable for this problem that requires only O(N) operations (N is of the order of the number of views). We analyze and demonstrate the high performance of the algorithm but show that the performance of the algorithm depends strongly on an appropriate choice of system parameters. These parameters, the number of views Nθ, and the detector spacing Δs are shown to be linked, and a choice of Δs strongly constrains the choice of Nθ. We show how an optimum Nθ can be determined for a fixed Δs, including practical values of Δs. A series of experiments that reinforce the theory is simulated on a computer.

© 1988 Optical Society of America

History
Original Manuscript: February 5, 1987
Manuscript Accepted: October 16, 1987
Published: March 1, 1988

Citation
Henry Stark and Hui Peng, "Shape estimation in computer tomography from minimal data," J. Opt. Soc. Am. A 5, 331-343 (1988)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-5-3-331


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References

  1. G. T. Herman, Image Reconstruction from Projections—The Fundamentals of Computerized Tomography (Academic, New York, 1980), Chaps. 8 and 10.
  2. H. Stark, J. W. Woods, I. Paul, R. Hingorani, “Direct Fourier reconstruction in computer tomography,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 237–245 (1981). [CrossRef]
  3. B. P. Medoff, “Image reconstruction from limited data,” doctoral dissertation (Stanford University, Stanford, Calif., 1983).
  4. B. P. Medoff, “Image reconstruction from limited data: theory and application in computer tomography,” in Image Recovery: Theory and Applications, H. Stark, ed. (Academic, Orlando, Fla., 1987), Chap. 7.
  5. R. M. Lewitt, R. H. T. Bates, “Image reconstruction from projections: IV. Projection completion methods (computational examples),” Optik 50, 269–278 (1978).
  6. I. Sezan, H. Stark, “Tomographic image reconstruction from incomplete view data by convex projections and direct Fourier inversion,” IEEE Trans. Med. Imag. TMI-3, 91–98 (1984). [CrossRef]
  7. K. C. Tam, V. Pérez-Méndez, “Tomographic imaging with limited-angle input,” J. Opt. Soc. Am. 71, 582–592 (1981). [CrossRef]
  8. T. Inouye, “Image reconstruction with limited view angle projections,” in Proceedings of the International Workshop on Physics and Engineering in Medical Imaging (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 165–168. [CrossRef]
  9. K. Hanson, “Bayesian and related methods in image reconstruction from incomplete data,” in Image Recovery: Theory and Applications, H. Stark, ed. (Academic, Orlando, Fla., 1987), Chap. 3.
  10. D. C. Youla, H. Webb, “Image restoration by the method of convex projections. Part I. Theory,” IEEE Trans. Med. Imag. TMI-1, 81–94 (1982). [CrossRef]
  11. G. T. Herman, Image Reconstruction from Projections—The Fundamentals of Computerized Tomography (Academic, New York, 1980), Chap. 1.
  12. There are other algorithms for shape estimation. For a partial list see S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983), pp. 106–107.

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