Geodesic
Comparison of two algorithms for the numerical solution of the two-dimensional vector tomography
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 90-108

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We compare two algorithms for reconstruction the vector fields from the known values of the ray transforms. The first algorithm is based on the least square method, approximating sequence is constructed with using the $B$-splines. The second algorithm is based on the method of singular value decomposition of operators of ray transforms, basis vector fields are constructed with using the harmonic polynomials and Jacobi polynomials.
Keywords: vector tomography, solenoidal field, potential field, approximation, ray transforms, least square method, $B$-splines
Mots-clés : singular value decomposition, orthogonal polynomials. 
@article{SEMR_2013_10_a55,
     author = {I. E. Svetov and A. P. Polyakova},
     title = {Comparison of two algorithms for the numerical solution of the two-dimensional vector tomography},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {90--108},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a55/}
}
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I. E. Svetov; A. P. Polyakova. Comparison of two algorithms for the numerical solution of the two-dimensional vector tomography. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 90-108. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a55/