Inverse Scattering Approach on Tomography Problem Using Multi-frequency Data

TL;DR

This paper presents a multi-frequency inverse scattering method using finite element and boundary integral techniques to reconstruct optical properties of biological tissues, improving initial guesses via recursive linearization.

Contribution

It introduces a recursive linearization algorithm combined with finite element and Nyström methods for enhanced tissue tomography from multi-frequency data.

Findings

Successful reconstruction in numerical examples

Effective initial guess via Born approximation

Improved accuracy with recursive wave number increments

Abstract

An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary integral method and added suitable boundary conditions on the surface of the domain. The initial guess is obtained by Born approximation based on the fact of weak scattering. The reconstruction is then improved each time by an increment on wave number. Finite element method is used for the interior domain containing inhomogeneity. Nystr\"om method is used for setting up the boundary conditions and jump conditions. Two numerical examples are presented.