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Regularization Problems in 3-D Ray Tomography

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Abstract

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.

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REFERENCES

  1. A. L. Buchgeim, Introduction to the Theory of Inverse Problems [in Russian], Novosibirsk (1988).

  2. A. S. Alekseev, M. N. Lavrentiev, and N. G. Preobrazhenskii, Problems of Reconstruction Tomography [in Russian], Novosibirsk (1985).

  3. G. A. Ryzhikov and V. N. Troyan, Tomography and Inverse Problems of Remote Sensing [in Russian], St. Petersburg (1994).

  4. G. I. Marchuk, Methods in Numerical Mathematics [in Russian], Moscow (1989).

  5. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Incorrect Problems [in Russian], Moscow (1987).

  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).

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Authors and Affiliations

  1. St.Petersburg State University, Russia

    V. N. Troyan & G. A. Ryzhikov

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  1. V. N. Troyan
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  2. G. A. Ryzhikov
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Troyan, V.N., Ryzhikov, G.A. Regularization Problems in 3-D Ray Tomography. Journal of Mathematical Sciences 108, 859–862 (2002). https://doi.org/10.1023/A:1013271817538

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  • DOI: https://doi.org/10.1023/A:1013271817538

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