Geodesic
Singular value decomposition of a normal Radon transform operator acting on 3D symmetric 2-tensor fields
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1572-1595

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A problem of 3D 2-tensor field potential part reconstruction by the known value of its normal Radon transform is considered. A singular value decomposition of the operator is constructed for solving the problem. Basic fields are constructed with the use of Jacobi polynomials, Gegenbauer polynomials, and spherical harmonics.
Keywords: symmetric tensor field, potential field, potential, singular value decomposition of an operator, system of orthogonal polynomials.
Mots-clés : normal Radon transform 
@article{SEMR_2021_18_2_a74,
     author = {A. P. Polyakova},
     title = {Singular value decomposition of a normal {Radon} transform operator acting on {3D} symmetric 2-tensor fields},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1572--1595},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a74/}
}
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A. P. Polyakova. Singular value decomposition of a normal Radon transform operator acting on 3D symmetric 2-tensor fields. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1572-1595. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a74/