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

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.