Geodesic
Reconstruction of a~singular support of a~tensor field given in refractive medium by its ray transform
Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 3, pp. 11-25

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We propose approaches to a numerical solution for the reconstruction problem of a singular support of a tensor field by its known ray transform. For the posed problem solving we use back-projection operators acting on the ray transforms and tensor analysis methods for Riemannian manifold. Indicator operators of the medium inhomogeneity are constructed and allow allocate the sets of points belonging to the singular support of scalar, vector and tensor fields. The algorithms for solving of the posed problem are proposed and realized.
Keywords: tomography, tensor field, function break, singular support, ray transform, back-projection operator, tensor analysis.
Mots-clés : refraction 
@article{SJIM_2015_18_3_a1,
     author = {E. Yu. Derevtsov and S. V. Maltseva},
     title = {Reconstruction of a~singular support of a~tensor field given in refractive medium by its ray transform},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {11--25},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2015_18_3_a1/}
}
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E. Yu. Derevtsov; S. V. Maltseva. Reconstruction of a~singular support of a~tensor field given in refractive medium by its ray transform. Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 3, pp. 11-25. http://geodesic.mathdoc.fr/item/SJIM_2015_18_3_a1/