This article is cited in 11 papers

Reconstruction of 2-tensor fields, given in a unit circle, by their ray transforms based on LSM with $B$-splines

I. E. Svetov^ab, A. P. Polyakova<sup>b

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University, Novosibirsk

Abstract: The numerical method for solving a tensor tomography problem of reconstructing a symmetric 2-tensor field, given in a unit circle, is offered. Potential and (or) solenoidal part of the desired field with fixed properties on the boundary are found from transverse and (or) 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.

Key words: tensor tomography, potential field, solenoidal field, least-squares method, $B$-splines, approximation, fast Fourier transform.

UDC: 514.8+517.983+519.6

Received: 15.05.2009
Revised: 13.07.2009

 English version: Numerical Analysis and Applications, 2010, 3:2, 151–164

Bibliographic databases:

•