Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems
Provides theoretical guarantees for regularization in inverse scattering, relevant for researchers in inverse problems and electromagnetic imaging.
This paper establishes variational source conditions for inverse electromagnetic medium scattering problems, yielding logarithmic convergence rates for regularization methods like Tikhonov regularization and improving conditional stability estimates.
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.