Reconstruction of 2d Symmetric 2-Tensor Field by Momentum Ray Transforms

Algorithms for reconstructing a two-dimensional symmetric 2-tensor field from the known longitudinal or transverse ray transforms of its moments are proposed and justified. The algorithms are based on the method of singular value decomposition. We use the known singular value decompositions of the Radon transform of functions and the ray transforms of 2-tensor fields. Numerical simulations demonstrate reliable results of reconstructing symmetric 2-tensor fields from values of the momentum ray transforms