Geodesic
Inversion formulas for tensor imaging on incomplete data
Daghestan Electronic Mathematical Reports, Tome 2 (2014), pp. 75-86

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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. 
@article{DEMR_2014_2_a5,
     author = {Z. G. Medzhidov},
     title = {Inversion formulas for tensor imaging on incomplete data},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {75--86},
     publisher = {mathdoc},
     volume = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2014_2_a5/}
}
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Z. G. Medzhidov. Inversion formulas for tensor imaging on incomplete data. Daghestan Electronic Mathematical Reports, Tome 2 (2014), pp. 75-86. http://geodesic.mathdoc.fr/item/DEMR_2014_2_a5/