Numerical B-spline solution of emission and vector 2D-tomography problems for media with absorption and refraction

A method of numerical solution for the tomography problems setting in a with medium with refraction and absorption is suggested. Namely, scalar or vector field by its ray transform calculated along geodesics of a Riemannian metric is reconstructed. The approximation of the solution is determined with usage of the least squares method. As bases we use the local bases of scalar and vector fields constructed by means of two-dimensional B-splines. Influence (on accuracy of reconstruction) such factors as smoothness of the required fields, curvature of the metrics and character of change of absorption coefficient, degree of digitization of data, an order and quantity of bases B-splines, various ways of construction of the local bases was numerically investigated.