Geodesic
Numerical realization of the algorithm of reconstruction of an inhomogeneous medium for an X-ray tomography problem
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 1, pp. 8-17

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

We study an X-ray tomography problem which is an inverse problem for the differential transport equation. We take into account the absorption of particles by the medium and their single scattering. The statement of the problem corresponds to multiple probing. The medium is unknown; the densities of the output flux averaged over energy are given. The object in question is the discontinuity surfaces of the coefficients of the equation. This corresponds to searching for the boundaries between various substances contained in the medium that we probe. The solution is constructive, and a version of numerical realization of the algorithm is presented.
Keywords: free boundary, inverse problem, multiple probing, tomography.
Mots-clés : transport equation 
@article{SJIM_2014_17_1_a1,
     author = {E. Yu. Balakina},
     title = {Numerical realization of the algorithm of reconstruction of an inhomogeneous medium for an {X-ray} tomography problem},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {8--17},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2014_17_1_a1/}
}
TY  - JOUR
AU  - E. Yu. Balakina
TI  - Numerical realization of the algorithm of reconstruction of an inhomogeneous medium for an X-ray tomography problem
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2014
SP  - 8
EP  - 17
VL  - 17
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2014_17_1_a1/
LA  - ru
ID  - SJIM_2014_17_1_a1
ER  - 
%0 Journal Article
%A E. Yu. Balakina
%T Numerical realization of the algorithm of reconstruction of an inhomogeneous medium for an X-ray tomography problem
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2014
%P 8-17
%V 17
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2014_17_1_a1/
%G ru
%F SJIM_2014_17_1_a1
E. Yu. Balakina. Numerical realization of the algorithm of reconstruction of an inhomogeneous medium for an X-ray tomography problem. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 1, pp. 8-17. http://geodesic.mathdoc.fr/item/SJIM_2014_17_1_a1/