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This article is cited in 2 scientific papers (total in 2 papers)
Inversion formulas for tensor imaging on incomplete data
Z. G. Medzhidov Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
Abstract:
In this article new inverse formulas for a ray transform of symmetric tensor fields with incomplete data are given. The Radon transform of Saint-Venant operator of tensor field is uniquely determined when the line integrals of the field along lines which form an $n$-dimensional complexes in the space $\mathbb{R}^n$ are given. Three most common complexes are considered: the family of lines intersecting a given curve, intersecting a given curve at infinity and tangent a given surface. In the case of the complex of lines intersecting a curve at infinite the formula, containing only two-fold integration is obtained.
Keywords:
symmetric tensor field, ray transform, reconstruction formula, complex of lines, Radon transform, solenoidal part, Saint-Venant operator.
Received: 03.11.2014 Revised: 22.12.2014 Accepted: 23.12.2014
Citation:
Z. G. Medzhidov, “Inversion formulas for tensor imaging on incomplete data”, Daghestan Electronic Mathematical Reports, 2014, no. 2, 75–86
Linking options:
https://www.mathnet.ru/eng/demr12 https://www.mathnet.ru/eng/demr/y2014/i2/p75
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Abstract page: | 119 | Full-text PDF : | 28 | References: | 28 |
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