Geodesic
Approximate solution of two-dimensional 2-tensor tomography problem using truncated singular value decomposition
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 480-499

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We propose a numerical solution of reconstruction problem of 2-tensor field in a unit disk from its known values of the ray transforms. The algorithm is based on the method of truncated singular value decomposition. Numerical simulations demonstrate an efficiency of the proposed approach. In addition, we compare proposed algorithm with an algorithm based on the least squares method where we use a finite basis consisting of $B$-splines as basis functions.
Keywords: 2-tensor tomography, solenoidal field, potential field, approximation, ray transforms, truncated singular value decomposition, least squares method, $B$-splines.
Mots-clés : orthogonal polynomials 
@article{SEMR_2015_12_a72,
     author = {I. E. Svetov and A. P. Polyakova},
     title = {Approximate solution of two-dimensional 2-tensor tomography problem using truncated singular value decomposition},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {480--499},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a72/}
}
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I. E. Svetov; A. P. Polyakova. Approximate solution of two-dimensional 2-tensor tomography problem using truncated singular value decomposition. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 480-499. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a72/