Geodesic
Reconstruction of three-dimensional vector fields based on values of normal, longitudinal, and weighted Radon transforms
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 4, pp. 125-142

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

The paper considers the vector tomography problem of reconstructing a three-dimensional vector field based on the values of unweighted (normal and longitudinal) and weighted Radon transforms. Using the detailed decomposition of vector fields obtained in the paper, connections are established between the unweighted and weighted Radon transforms acting on vector fields and the Radon transform acting on functions. In particular, the kernels of tomographic integral operators acting on vector fields are described. Some statements of tomography problems for the reconstruction of vector fields are considered, and inversion formulas for their solution are obtained.
Keywords: vector tomography, decomposition of vector field, weighted Radon transform
Mots-clés : normal Radon transform, longitudinal Radon transform, inversion formula. 
@article{SJIM_2023_26_4_a8,
     author = {I. E. Svetov and A. P. Polyakova},
     title = {Reconstruction of three-dimensional vector fields based on values of normal, longitudinal, and weighted {Radon} transforms},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {125--142},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a8/}
}
TY  - JOUR
AU  - I. E. Svetov
AU  - A. P. Polyakova
TI  - Reconstruction of three-dimensional vector fields based on values of normal, longitudinal, and weighted Radon transforms
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2023
SP  - 125
EP  - 142
VL  - 26
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a8/
LA  - ru
ID  - SJIM_2023_26_4_a8
ER  - 
%0 Journal Article
%A I. E. Svetov
%A A. P. Polyakova
%T Reconstruction of three-dimensional vector fields based on values of normal, longitudinal, and weighted Radon transforms
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2023
%P 125-142
%V 26
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a8/
%G ru
%F SJIM_2023_26_4_a8
I. E. Svetov; A. P. Polyakova. Reconstruction of three-dimensional vector fields based on values of normal, longitudinal, and weighted Radon transforms. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 4, pp. 125-142. http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a8/