Acceleration techniques for regularized Newton methods applied to electromagnetic inverse medium scattering problems

We study the construction and updating of spectral preconditioners for regularized Newton methods and their application to electromagnetic inverse medium scattering problems. Moreover, we show how a Lepski\u{i}-type stopping rule can be implemented efficiently for these methods. In numerical examples, the proposed method compares favorably with other iterative regularization method in terms of work-precision diagrams for exact data. For data perturbed by random noise, the Lepski\u{i}-type stopping rule performs considerably better than the commonly used discrepancy principle.