Abstract: We consider the problem of recovery of a three-dimensional vector field in the cylinder [1]. The data for the problem are two-dimensional integral ray transforms and NMR-data [2]. We explain the features of this problem in the cases of different vector fields and present algorithms for solving. Simulation showed good results. This work was supported by the Russian Foundation for Basic Research (RFBR) and the German Science Foundation (DFG) according to the joint German-Russian research project 19-51-12008. References 1. Derevtsov E. Yu., Maltseva S. V. Recovery of a vector field in the cylinder by its jointly known NMR-images and ray transforms // Siberian Electronic Mathematical Reports. 2021. V. 18 (1). P. 86-103. 2. S.V. Maltseva, A.A. Cherevko, A.K. Khe, A.E. Akulov, A.A. Savelov, A.A. Tulupov, E.Yu. Derevtsov, M.P. Moshkin, A.P. Chupakhin. Reconstruction of Complex Vasculature by Varying the Slope of the Scan Plane in High-Field Magnetic Resonance Imaging // Applied Magnetic Resonance, 47:1 (2016), pp 23-39.

Cite: Derevtsov E.Y. , Malʹtseva S.V.
Recovery of a vector field in the cylinder by 2D ray transforms and NMR-data
In compilation International Conference «Marchuk Scientific Readings 2020» (MSR-2020), dedicated to the 95th anniversary of the birthday of RAS Academician Guri. I. Marchuk October 19 - 23, 2020, Akademgorodok, Novosibirsk, Russia. 2021. – Т.1715. – C.135. DOI: 10.24412/CL-35064-2021-190

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