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

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.

arXiv commentinverse scattering, Maxwell equations, stability, regularization, source condition

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Cited by in corpus (6)

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• Convergence Analysis of (Statistical) Inverse Problems under Conditional Stability Estimates
• Hölder-logarithmic stability in Fourier synthesis
• Dual gradient method for ill-posed problems using multiple repeated measurement data
• Numerical reconstruction from the Fourier transform on the ball using prolate spheroidal wave functions