A linearised inverse conductivity problem for the Maxwell system at a high frequency

TL;DR

This paper investigates a high-frequency linearised inverse conductivity problem for electromagnetic waves, deriving stability bounds and proposing a Fourier-based reconstruction algorithm validated through numerical experiments.

Contribution

It introduces increasing stability bounds for the inverse problem at high frequencies and develops a Fourier mode reconstruction method validated numerically.

Findings

Stability bounds improve with frequency, showing increased resolution.

Numerical experiments confirm the theoretical stability and resolution enhancement.

Reconstruction algorithm effectively recovers Fourier modes of conductivity at high frequencies.

Abstract

We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system and in a simplified transverse electric mode are derived. These bounds contain a Lipschitz term with a factor growing polynomially in terms of the frequency, a Holder term, and a logarithmic term which decays with respect to the frequency as a power. To validate this increasing stability numerically, we propose a reconstruction algorithm aiming at the recovery of sufficiently many Fourier modes of the conductivity. A numerical evidence sheds light on the influence of the growing frequency and confirms the improved resolution at higher frequencies.