Advertisement

Cone beam reconstruction and fourier transform of distributions

  • Oleg Trofimov
Reconstruction from Projections
Part of the Lecture Notes in Computer Science book series (LNCS, volume 719)

Abstract

For distributions, that are the Fourier transforms of cone-beam x-ray data, there are given formulas that allow to create numerical algorithms on base of the Kirillov-Tuy inversion formulas.

Key words

cone-beams reconstruction distributions Fourier transforms 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. V. Finch. Cone beam reconstruction with sources on a curve. SIAM. J. APPL. MATH. 1985, vol.45, No 4, 665–671.Google Scholar
  2. 2.
    A.S. Denisjuk. An inversion of generalized Radon's transform (in print)Google Scholar
  3. 3.
    I. M. GELFAND, A. B. GONCHAROV. Reconstruction of a finite function from its integrals on lines intersecting a set of points in the space. Dokl. Akad. Nauk SSSR, 290(1986), pp. 1037–1040.Google Scholar
  4. 4.
    I.M. Gelfand, G.E. Shilov. Distributions, v.1, Distributions and actions over them, Moscow, 1959Google Scholar
  5. 5.
    P. Grangeat. Analyse d'une système d'imagerie 3D par reconstruction a pàrtier de radiographies X en géometrie conqué. These de doctorat, Grenoble, 1987.Google Scholar
  6. 6.
    A. A. KIRILLOV. On a problem of I. M. Gel'fand, Dokl. Akad. Nauk SSSR, 37(1961), pp.276–277; Eng. trans. Soviet Math. Dokl., 2(1961), pp.268–269.Google Scholar
  7. 7.
    F. Natterer. The mathematics of computerized tomography. B. G. Teubner, Stuttgart, and John Wiley & Sons Ltd, 1986.Google Scholar
  8. 8.
    V. I. Semyanisti. Homogeneous functions and some problems of integral geometry in spaces of constant curvature, Dokl. Akad. Nauk SSSR, 136(1961), pp. 288–291; Eng. trans. Soviet Math. Dokl., 2(1961), pp.59–62.Google Scholar
  9. 9.
    K.K. Smirnov, O.E. Trofimov. Reconstrution of the density function from its line integrals. Conference “Automation of scientific researches on base applications of computers”, (abstracts), Institute of Automation and Electrometry, Siberian Branch of Academy of Sciences USSR. Novosibirsk, 1979.Google Scholar
  10. 10.
    B.D. Smith. Image reconstruction from cone-beam projections necessary and sufficient conditions and reconstruction methods. IEEE Trans. Med. Image. MI-4, 14–28(1985).Google Scholar
  11. 11.
    B.D. Smith. Cone-beam tomography: recent advances and a tutorial review. Optical Engenering, May 1990, Vol 29, N5, pp. 524–534.Google Scholar
  12. 12.
    O.E. Trofimov, L.W. Tiurenkova. One method numerical reconstrution of the density function from its tomogramm. Preprint M. 440, Institute of Automation and Electrometry, Siberian Branch of Academy of Sciences USSR. Novosibirsk, 1989.Google Scholar
  13. 13.
    H. K. Tuy. An inversion formula for cone-beam reconstruction. SIAM. J. APPL. MATH. 1983, vol.43, No 3, 546–552.Google Scholar
  14. 14.
    W.T. Zhirnov, K.K. Smirnov, O.E. Trofimov. Numerical methods in tomography, in “Methods and means of image processing” proceedings of Institute of Automation and Electrometry, Siberian Branch of Academy of Sciences USSR. Novosibirsk, 1982Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Oleg Trofimov
    • 1
  1. 1.Institute of Automation and ElectrometrySiberian Branch of Russian Academy of SciencesNovosibirskRussia

Personalised recommendations