A hybrid finite element/finite difference method for reconstruction of dielectric properties of conductive objects

TL;DR

This paper introduces a hybrid finite element/finite difference approach for reconstructing electromagnetic properties of breast tissue, aiding tumor detection by solving an ill-posed inverse problem with optimization techniques.

Contribution

It presents a novel hybrid numerical method combining finite element and finite difference techniques for electromagnetic property reconstruction in breast tissue.

Findings

Effective reconstruction of dielectric properties demonstrated

Hybrid method improves accuracy over traditional approaches

Adaptive mesh refinement enhances solution precision

Abstract

The aim of this article is to present a hybrid finite element/finite difference method which is used for reconstructions of electromagnetic properties within a realistic breast phantom. This is done by studying the mentioned properties' (electric permittivity and conductivity in this case) representing coefficients in a constellation of Maxwell's equations. This information is valuable since these coefficient can reveal types of tissues within the breast, and in applications could be used to detect shapes and locations of tumours. Because of the ill-posed nature of this coefficient inverse problem, we approach it as an optimization problem by introducing the corresponding Tikhonov functional and in turn Lagrangian. These are then minimized by utilizing an interplay between finite element and finite difference methods for solutions of direct and adjoint problems, and thereafter by applying a conjugate gradient method to an adaptively refined mesh.