Geodesic
Reconstruction of a vector field from the data of its longitudinal and transverse ray transforms
Daghestan Electronic Mathematical Reports, Tome 16 (2021), pp. 62-73.

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An algorithm for the complete reconstruction of a vector field in three-dimensional Euclidean space based on incomplete integral data of a longitudinal and a transverse ray transforms is constructed. From of data of a longitudinal ray transform given on the family of straight lines intersecting a piecewise smooth curve, the solenoidal part of the vector field is constructed, and from of data of a transverse ray transform, the potential of an unknown field is constructed. The problem of reconstruction is also solved in the case of a family of lines intersecting a curve at infinity.
Keywords: Radon transformation, longitudinal ray transform, transverse ray transform, inversion formula. 
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Z. G. Medzhidov. Reconstruction of a vector field from the data of its longitudinal and transverse ray transforms. Daghestan Electronic Mathematical Reports, Tome 16 (2021), pp. 62-73. http://geodesic.mathdoc.fr/item/DEMR_2021_16_a4/

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