Abstract
We propose some approaches for numerically solving the problem of reconstructing the singular support of a symmetric tensor field, given in a refracting medium, by its known ray transform. To solve the problem, we use the back-projection operators that act on the ray transforms and the tensor analysis methods on Riemannian manifolds. We construct the operators of the medium inhomogeneity indicator that allow us to identify the sets of points of the singular support of the scalar, vector, and tensor fields. We propose and implement algorithms for solving the problem under study.
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Original Russian Text © E.Yu. Derevtsov, S.V. Maltseva, 2015, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2015, Vol. XVIII, No. 3, pp. 11–25.
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Derevtsov, E.Y., Maltseva, S.V. Reconstruction of the singular support of a tensor field given in a refracting medium by its ray transform. J. Appl. Ind. Math. 9, 447–460 (2015). https://doi.org/10.1134/S1990478915040018
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DOI: https://doi.org/10.1134/S1990478915040018