The method of approximate inverse for ray transform operators on two-dimensional symmetric $m$-tensor fields

I. E. Svetov; A. P. Polyakova; S. V. Maltseva

Geodesic

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The method of approximate inverse for ray transform operators on two-dimensional symmetric $m$-tensor fields

I. E. Svetov ; A. P. Polyakova ; S. V. Maltseva

Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 1, pp. 104-115

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Résumé

Two approaches are proposed for recovering a symmetric $m$-tensor field in a unit disk from the given values of ray transforms. The approaches are based on the method of approximate inverse. The first approach allows us to reconstruct all components of the tensor field, while the second recovers the potentials of the solenoidal part and $m$ potential parts of the tensor field.

Keywords: tensor tomography, method of approximate inverse, adjoint operator, ray transform, tensor field, potential.
Mots-clés : Radon transform

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     title = {The method of approximate inverse for ray transform operators on two-dimensional symmetric $m$-tensor fields},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2019_22_1_a9/}
}

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I. E. Svetov; A. P. Polyakova; S. V. Maltseva. The method of approximate inverse for ray transform operators on two-dimensional symmetric $m$-tensor fields. Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 1, pp. 104-115. http://geodesic.mathdoc.fr/item/SJIM_2019_22_1_a9/