Robust Iterative Permittivity Inversion With Projection-Based Reduced Order Models

In this article, we study the application of reduced order models (ROMs) for permittivity inversion to address the high nonlinearity and cycle-skipping effects in inverse scattering problems (ISPs). In this approach, ROMs are constructed through the Galerkin approximation of wave operators. The ROM-based data to Born (DtB) process generates Born data and can be incorporated with a back projection (BP) inversion scheme. We implement an iterative BP inversion scheme integrated with the layer-peeling (LP) strategy to ensure stable convergence. Additionally, we incorporate regularization techniques to enhance the algorithm’s robustness, especially in noisy environments. The performance of the proposed approach is demonstrated through numerical examples.