IPI
Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems
Frederic Weidling Thorsten Hohage
Inverse Problems & Imaging 2017, 11(1): 203-220 doi: 10.3934/ipi.2017010

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.

keywords: Inverse scattering Maxwell equations stability regularization source condition

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