Journal of Mathematical Sciences

, Volume 108, Issue 5, pp 859–862 | Cite as

Regularization Problems in 3-D Ray Tomography

  • V. N. Troyan
  • G. A. Ryzhikov


Relationships between Tikhonov's regularization, statistical regularization, and potential theory are considered. It is demonstrated that the use of Tikhonov's regularization leads to correlation operators such that they may be interpreted as the Coulomb or Yukawa potentials. Physical interpretation of the interaction of rays as ``charged'' threads with respective potentials is given. Bibliography: 6 titles.


Physical Interpretation Statistical Regularization Potential Theory Yukawa Potential Regularization Problem 
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  1. 1.
    A. L. Buchgeim, Introduction to the Theory of Inverse Problems [in Russian], Novosibirsk (1988).Google Scholar
  2. 2.
    A. S. Alekseev, M. N. Lavrentiev, and N. G. Preobrazhenskii, Problems of Reconstruction Tomography [in Russian], Novosibirsk (1985).Google Scholar
  3. 3.
    G. A. Ryzhikov and V. N. Troyan, Tomography and Inverse Problems of Remote Sensing [in Russian], St. Petersburg (1994).Google Scholar
  4. 4.
    G. I. Marchuk, Methods in Numerical Mathematics [in Russian], Moscow (1989).Google Scholar
  5. 5.
    A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Incorrect Problems [in Russian], Moscow (1987).Google Scholar
  6. 6.
    G. A. Ryzhikov and V. N. Troyan, "Determination of the wave field and the velocity in a medium by using the method of perturbation theory," Vestn. Leningrad Univ., 25, 23-31 (1986).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • V. N. Troyan
    • 1
  • G. A. Ryzhikov
    • 1
  1. 1.St.Petersburg State UniversityRussia

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