This article is cited in 1 paper

Proceedings of conferences

Reconstruction of solenoidal $2$-tensor fields, given in a unit disk, in their longitudinal ray transforms

I. E. Svetov

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

Abstract: The numerical method for solving a tensor tomography problem of reconstructing symmetric solenoidal $2$-tensor fields, given in a unit disk, is offered. Desired field with fixed properties on the boundary are found from longitudinal ray transforms, calculated along the straight lines crossing the support of the field. The solution is sought by means of the least-squares method with the use, as approximating sequence, of local bases constructed on the basis of $B$-splines. This algorithm was compared with algorithms based on inversion formulas for the accuracy of reconstruction.

Keywords: tensor tomography, solenoidal field, least-squares method, $B$-splines, approximation, fast Fourier transform, inversion formula.

UDC: 514.8, 517.983, 519.6

MSC: 44A30

Received March 6, 2010