Inversion formulas for recovering the harmonic 2D-vector field by known ray transforms
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 436-446.

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

We obtained the inversion formulas for recovering the harmonic 2D-vector field given in unit disk by known ray transforms.
Keywords: vector field, solenoidal field, potential field, harmonic field, longitudinal ray transform, harmonic polynomials.
Mots-clés : inversion formula, transverse ray transform, Radon transform
@article{SEMR_2015_12_a85,
     author = {I. E. Svetov},
     title = {Inversion formulas for recovering the harmonic {2D-vector} field by known ray transforms},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {436--446},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a85/}
}
TY  - JOUR
AU  - I. E. Svetov
TI  - Inversion formulas for recovering the harmonic 2D-vector field by known ray transforms
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2015
SP  - 436
EP  - 446
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2015_12_a85/
LA  - ru
ID  - SEMR_2015_12_a85
ER  - 
%0 Journal Article
%A I. E. Svetov
%T Inversion formulas for recovering the harmonic 2D-vector field by known ray transforms
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2015
%P 436-446
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2015_12_a85/
%G ru
%F SEMR_2015_12_a85
I. E. Svetov. Inversion formulas for recovering the harmonic 2D-vector field by known ray transforms. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 436-446. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a85/

[1] V. Romanov, Inverse Problems of Mathematical Physics, VSP, Utrecht, 1984 | MR

[2] V. A. Sharafutdinov, Integral Geometry of Tensor Fields, VSP, Utrecht, 1994 | MR

[3] S. R. Deans, The Radon Transform And Some Of Its Applications, John Wiley Sons, New York, 1983 | MR | Zbl

[4] I. E. Svetov, E. Yu. Derevtsov, Yu. S. Volkov, T. Schuster, “A numerical solver based on B-splines for 2D vector field tomography in a refracting medium”, Mathematics and Computers in Simulation, 97 (2014), 207–223 | DOI | MR

[5] T. Schuster, “20 years of imaging in vector field tomography: a review”, Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT), Publications of the Scuola Normale Superiore, CRM Series, 7, eds. Y. Censor, M. Jiang, A. K. Louis, Birkhäuser, 2008, 389–424 | MR

[6] H. Weyl, “The method of orthogonal projection in potential theory”, Duke Mathematical Journal, 7 (1940), 411–444 | DOI | MR

[7] A. N. Tihonov, A. A. Samarsky, Equations of Mathematical Physics, 6th edition, Puplishing MSU, M., 1999 (in Russian)

[8] I. S. Gradshtein, I. M. Ryzhik, Tables of integrals, series and products, 4th edition, State publishing physical and mathematical literature, M., 1963 (in Russian)