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Topics in Analysis and its Applications pp 365–375Cite as

On Mathematical Problems of Two-Dimensional Tomography

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Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry ((NAII,volume 147))

Abstract

In this paper the problem of restoring the inside construction of an object by its X-ray pictures is considered. We limit ourself on discussing the two dimensional case. Let us note that just this case is used in acting medical tomography devices. The problem is to find the formulas, which as good as possible restore the density, having on hand the X-ray pictures for a finite number of directions only and which are steady for L2(−1, 1) distortions of the projections.

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References

  1. Helgason, S. (1984) Groups and geometric analysis, Integral geometry, invariant di erential operators, and spherical functions, Academic Press, Orlando.

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  2. Natterer, F. (1986) The mathematics of computerized tomography, B.G. Teubner, Stuttgart; John Wiley, Chichester.

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  3. Gelfand, I.M. and Gindikin, S.G. (1990) Mathematical problems of tomography, Amer. Math. Soc., Providence, RI.

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  4. Landkof, N.S. (1966) The bases of the modern potential theory, Nauka, Moscow (Russian).

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  5. Logan, B.F. and Shepp, L.A. (1975) Optimal reconstruction of a function from its projections, Duke Math. J., Vol. 42, pp. 645–659.

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Author information

Authors and Affiliations

  1. Institute of Matematics of National Academy of Sciences of Armenia, 24-b Marshal Bargramian ave., Yerevan, 375019, Armenia

    A Vagarshakyan

Authors
  1. A Vagarshakyan
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Editor information

Editors and Affiliations

  1. Institute of Mathematics of National Academy of Sciences of Armenia, Yerevan, Armenia

    G. A. Barsegian

  2. Mathematical Institute, Freie Universität Berlin, Berlin, Germany

    H. G. W. Begehr

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© 2004 Kluwer Academic Publishers

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Vagarshakyan, A. (2004). On Mathematical Problems of Two-Dimensional Tomography. In: Barsegian, G.A., Begehr, H.G.W. (eds) Topics in Analysis and its Applications. NATO Science Series II: Mathematics, Physics and Chemistry, vol 147. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2128-3_25

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