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

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.