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

TL;DR

This paper develops spectral preconditioners and an efficient stopping rule for regularized Newton methods, improving electromagnetic inverse medium scattering reconstructions, especially with noisy data.

Contribution

It introduces spectral preconditioners and a Lepskii-type stopping rule tailored for electromagnetic inverse problems, enhancing computational efficiency and noise robustness.

Findings

Proposed method outperforms other iterative regularization techniques in accuracy and efficiency.

Lepskii-type stopping rule is more effective than discrepancy principle with noisy data.

Numerical examples demonstrate superior performance in electromagnetic inverse medium scattering reconstructions.

Abstract

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.