Geodesic
Reconstruction of solenoidal part of a~three-dimensional vector field by its ray transforms along straight lines, parallel to the coordinate planes
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 3, pp. 329-344

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The numerical solution of a vector field reconstruction problem is offered. It is assumed that a field is given in a unit ball. The approximation of the solenoidal part of the vector field is constructed from ray transforms known over all the straight lines parallel to one of the coordinate planes. Good results of reconstruction of solenoidal vector fields by the numerical simulations are proposed. 
@article{SJVM_2012_15_3_a8,
     author = {I. E. Svetov},
     title = {Reconstruction of solenoidal part of a~three-dimensional vector field by its ray transforms along straight lines, parallel to the coordinate planes},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {329--344},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_3_a8/}
}
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I. E. Svetov. Reconstruction of solenoidal part of a~three-dimensional vector field by its ray transforms along straight lines, parallel to the coordinate planes. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 3, pp. 329-344. http://geodesic.mathdoc.fr/item/SJVM_2012_15_3_a8/