Numerical reconstruction of a two-dimensional vector field from momentum ray transforms

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

Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 4, pp. 113-129

Résumé

The algorithms for reconstructing a vector field from known longitudinal or transverse ray transforms of its moment are proposed and justified. The properties of several algorithms are studied depending on the degree of data discretization, the level and type of noise introduced into the data, the smoothness of the vector field, and the degree of connectivity of its support. Numerical simulations show good results of reconstructing vector fields from their momentum ray transforms.

Détail

Keywords: vector field, momentum ray transform, differential property of ray transforms, approximation, numerical simulation.
Mots-clés : reconstruction algorithm

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