This article is cited in 4 papers

Proceedings of conferences

Certain problems of non-scalar tomography

E. Yu. Derevtsov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: Certain problems of scalar, vector and tensor tomography are considered in the paper. Main tools and results of scalar tomography are formulated and connected with the similar in area of tomography for tensor fields. Definitions and properties of differential and integral operators as well as different types of ray transforms for tensor fields are described. The inversion formulas are developed starting from scalar case to the tensor case. Results of few numerical simulations for reconstruction of tensor fields by its ray transforms are presented.

Keywords: tomography problem, vector field, tensor field, Radon transform, ray transform, decomposition theorem, back projection operator, inversion formulas, tensor analysis, numerical methods.

UDC: 517.9, 519.6

MSC: 44A30

Received March 10, 2010