Geodesic
The problem of single-beam probing of an unknown medium
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 2, pp. 21-27.

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

We propose an algorithm for determining the shadows of unknown bodies inside an arbitrary medium probed by radiation only in one direction. We demonstrate a successful performance of the algorithm in the case that on a direct visualization (a photograph) the bodies under consideration are indistinguishable. We study the problem of overlapping the shadows of some objects by others and conclude that this circumstance can improve or worsen the quality of reconstruction depending on the radiation characteristics of the medium. The presented results of numerical experiments show good agreement between theoretical and computational methods.
Keywords: radiation transfer equation, X-ray tomography. 
@article{SJIM_2011_14_2_a2,
     author = {D. S. Anikonov and V. G. Nazarov and I. V. Prokhorov},
     title = {The problem of single-beam probing of an unknown medium},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {21--27},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a2/}
}
TY  - JOUR
AU  - D. S. Anikonov
AU  - V. G. Nazarov
AU  - I. V. Prokhorov
TI  - The problem of single-beam probing of an unknown medium
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2011
SP  - 21
EP  - 27
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a2/
LA  - ru
ID  - SJIM_2011_14_2_a2
ER  - 
%0 Journal Article
%A D. S. Anikonov
%A V. G. Nazarov
%A I. V. Prokhorov
%T The problem of single-beam probing of an unknown medium
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2011
%P 21-27
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a2/
%G ru
%F SJIM_2011_14_2_a2
D. S. Anikonov; V. G. Nazarov; I. V. Prokhorov. The problem of single-beam probing of an unknown medium. Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 2, pp. 21-27. http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a2/

[1] Pikalov V. V., Melnikova T. S., Tomografiya plazmy, Nauka, Novosibirsk, 1995

[2] Anikonov D. S., Kovtanyuk A. E., Prokhorov I. V., Ispolzovanie uravneniya perenosa v tomografii, Logos, M., 2000

[3] Anikonov D. S., Nazarov V. G., Prokhorov I. V., Poorly Visible Media in X-ray Tomography, VSP, Utrecht–Boston, 2002

[4] G. I. Marchuk, G. A. Mikhailov, M. A. Nazarliev i dr. (red.), Metod Monte-Karlo v atmosfernoi optike, Nauka, Novosibirsk, 1976

[5] Ermakov S. M., Mikhailov G. A., Statisticheskoe modelirovanie, Nauka, M., 1982 | MR