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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{DEMR_2021_16_a4,
     author = {Z. G. Medzhidov},
     title = {Reconstruction of a vector field from the data of its longitudinal and transverse ray transforms},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {62--73},
     publisher = {mathdoc},
     volume = {16},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2021_16_a4/}
}
TY  - JOUR
AU  - Z. G. Medzhidov
TI  - Reconstruction of a vector field from the data of its longitudinal and transverse ray transforms
JO  - Daghestan Electronic Mathematical Reports
PY  - 2021
SP  - 62
EP  - 73
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DEMR_2021_16_a4/
LA  - ru
ID  - DEMR_2021_16_a4
ER  - 
%0 Journal Article
%A Z. G. Medzhidov
%T Reconstruction of a vector field from the data of its longitudinal and transverse ray transforms
%J Daghestan Electronic Mathematical Reports
%D 2021
%P 62-73
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DEMR_2021_16_a4/
%G ru
%F DEMR_2021_16_a4
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/