Geodesic
An Application of the SVD-Method to the Problem of Integral Geometry of 2-Tensor Fields
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 3, pp. 73-94

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A problem of integral geometry consisting in determination of a given in unit disk symmetric 2-tensor field by its known ray transforms is considered. Singular value decompositions (SVD) of the operators of longitudinal, transverse and mixed ray transforms that are the integrals of projections of a field at a line of integration are constructed. The results are based essentially on a theorem of a tensor field decomposition and its representation through potentials. The obtained singular value decompositions are constructive and are foundations for the algorithms of a tensor field reconstruction by its known ray transforms.
Keywords: tensor field, integral geometry, tensor tomography, ray transform. 
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     author = {E. Yu. Derevtsov and A. P. Polyakova},
     title = {An {Application} of the {SVD-Method} to the {Problem} of {Integral} {Geometry} of {2-Tensor} {Fields}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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E. Yu. Derevtsov; A. P. Polyakova. An Application of the SVD-Method to the Problem of Integral Geometry of 2-Tensor Fields. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 3, pp. 73-94. http://geodesic.mathdoc.fr/item/VNGU_2012_12_3_a6/