On iterative reconstruction in the nonlinearized polarization tomography

We give a uniqueness theorem and a reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomography data. We assume that the medium has uniform background parameters and that the anisotropic (dielectric permeability) perturbation is described by symmetric and sufficiently small matrix function f. On a pure mathematical level, this paper contributes to the theory of non-Abelian Radon transforms and to iterative methods of inverse scattering.