On iterative reconstruction in the nonlinearized polarization tomography

TL;DR

This paper presents a uniqueness theorem and an iterative reconstruction algorithm for determining dielectric anisotropy in a medium using polarization tomography, advancing mathematical understanding of inverse scattering and Radon transforms.

Contribution

It introduces a new uniqueness theorem and an iterative reconstruction method for nonlinear polarization tomography involving dielectric anisotropy.

Findings

Proves a uniqueness theorem for the inverse problem.

Develops an iterative reconstruction algorithm.

Contributes to the theory of non-abelian Radon transforms.

Abstract

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.