Geodesic
Reconstruction of vector fields and their singularities from ray transforms
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 1, pp. 29-46

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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. 
@article{SJVM_2011_14_1_a3,
     author = {E. Yu. Derevtsov and V. V. Pickalov},
     title = {Reconstruction of vector fields and their singularities from ray transforms},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {29--46},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a3/}
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E. Yu. Derevtsov; V. V. Pickalov. Reconstruction of vector fields and their singularities from ray transforms. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 1, pp. 29-46. http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a3/