Geodesic
Numerical solution of a~problem of refractive tomography in a~tube domain
Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 4, pp. 30-41

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A problem of refractive tomography is considered for a tube domain with a given arbitrary varying absorption and refraction of a special type modelled by means of a Riemannian metric. We propose a numerical solution of the problem based on the consecutive solution of a series of two-dimensional problems. We show that such an approach is possible if the domain has a sufficiently large family of totally geodesic submanifolds of dimension two. Riemannian metrics admitting the existence of the set are contructed. We propose an algorithm for an approximate solution of the problem based on the least squares method.
Keywords: tomography, Riemannian metric, ray transform, totally geodesic submanifold, least squares method.
Mots-clés : absorption, refraction 
@article{SJIM_2015_18_4_a3,
     author = {E. Yu. Derevtsov},
     title = {Numerical solution of a~problem of refractive tomography in a~tube domain},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {30--41},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2015_18_4_a3/}
}
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E. Yu. Derevtsov. Numerical solution of a~problem of refractive tomography in a~tube domain. Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 4, pp. 30-41. http://geodesic.mathdoc.fr/item/SJIM_2015_18_4_a3/