Abstract
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.
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