Computational mathematics

Recovery of a vector field in the cylinder by its jointly known NMR images and ray transforms

E. Yu. Derevtsov, S. V. Maltseva

Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia

Abstract: In the paper we consider a problem of recovering a 3D vector field given in cylinder by means of jointly known nuclear magnetic resonance (NMR) images and ray transforms. The NRM images and 2D longitudinal and transverse ray transforms are known in every plane orthogonal to the cylinder axis. The 3D ray transforms of new type connected with a family of the parallel planes are defined. Simulation confirms the legitimacy and further perspective of the proposed approach.

Keywords: vector field, cylindrical domain, NMR image, ray transform, inversion formula, boundary value problem, numerical simulation.

UDC: 517.983, 519.6

MSC: 65M32

Received November 20, 2020, published February 16, 2021

Language: English

DOI: 10.33048/semi.2021.18.008

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