Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems

TL;DR

This paper establishes variational source conditions for electromagnetic inverse scattering problems, leading to improved stability estimates and convergence rates for regularization methods in recovering the medium's refractive index.

Contribution

It introduces new variational source conditions for near and far field data, enhancing stability estimates and convergence analysis in electromagnetic inverse problems.

Findings

Logarithmic convergence rates for Tikhonov regularization.

Conditional stability estimates that improve existing results.

Applicability to both near and far field measurement data.

Abstract

This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two variational source conditions for near and far field data, which imply logarithmic rates of convergence of regularization methods, in particular Tikhonov regularization, as the noise level tends to $0$. Moreover, these variational source conditions imply conditional stability estimates which improve and complement known stability estimates in the literature.