  We give uniqueness theorem and 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 article contributes to
the theory of non-abelian Radon transforms and to iterative methods of inverse
scattering.
