Journal of Mathematical Sciences

, Volume 202, Issue 1, pp 50–71 | Cite as

Solution of the Integral Geometry Problem for 2-Tensor Fields by the Singular Value Decomposition Method

  • E. Yu. Derevtsov
  • A. P. Polyakova

We consider the integral geometry problem of finding a symmetric 2-tensor field in a unit disk provided that the ray transforms of this field are known. We construct singular value decompositions of the operators of longitudinal, transversal, and mixed ray transforms that are the integrals of projections of a field onto the line where they are computed. We essentially use the results on decomposition of tensor fields and their representation in terms of potentials. The singular value decompositions are constructive and can be used for creating an algorithm for recovering a tensor field from its known ray characteristics.


Radon Unit Disk Jacobi Polynomial Continuous Linear Operator Require Assertion 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Sobolev Institute of Mathematics SB RASNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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