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Reconstruction of vector fields and their singularities from ray transforms |
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| Authors: | E Yu Derevtsov V V Pickalov |
| Institution: | 1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia 2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia 3. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, ul. Institutskaya 4/1, Novosibirsk, 630090, Russia |
| Abstract: | In this paper, numerical methods for reconstruction of the singular support of a vector field from its known longitudinal and (or) transverse ray transforms are proposed. Apart from a modification for the Vainberg operator, we use integral operators of angular moments and back projections as well as differential operators of tensor analysis for solving the problem. Results of numerical simulation for reconstructing discontinuous vector fields and with discontinuities in the derivatives are presented. Visualization of their singular support is shown. |
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