An Application of the SVD-Method to the Problem of Integral Geometry of 2-Tensor Fields

A problem of integral geometry consisting in determination of a given in unit disk symmetric 2-tensor field by its known ray transforms is considered. Singular value decompositions (SVD) of the operators of longitudinal, transverse and mixed ray transforms that are the integrals of projections of a field at a line of integration are constructed. The results are based essentially on a theorem of a tensor field decomposition and its representation through potentials. The obtained singular value decompositions are constructive and are foundations for the algorithms of a tensor field reconstruction by its known ray transforms.