Sensitivity analysis for 3D Maxwell's equations and its use in the resolution of an inverse medium problem at fixed frequency

TL;DR

This paper develops a sensitivity analysis method for 3D Maxwell's equations to reconstruct small perturbations in a medium's electric properties from boundary measurements, enabling efficient inverse problem solutions.

Contribution

It introduces a non-iterative algorithm based on sensitivity analysis and explicit relations, improving reconstruction of perturbations in 3D electromagnetic models.

Findings

Successfully reconstructs perturbation location and volume in 3D models.

Demonstrates effectiveness on simple and realistic head models.

Provides explicit formulas linking measurements to perturbation characteristics.

Abstract

This paper deals with the reconstruction of small-amplitude perturbations in the electric properties (permittivity and conductivity) of a medium from boundary measurements of the electric field at a fixed frequency. The underlying model is the three-dimensional time-harmonic Maxwell equations in the electric field. Sensitivity analysis with respect to the parameters is performed, and explicit relations between the boundary measurements and the characteristics of the perturbations are found from an appropriate integral equation and extensive numerical simulations in 3D. The resulting non-iterative algorithm allows to retrieve efficiently the centre and volume of the perturbations in various situations from the simple sphere to a realistic model of the human head.