Speaker
Description
We consider an inverse scattering problem for monostatic synthetic aperture radar (SAR), where the goal is to estimate the wave speed in a heterogeneous, isotropic medium using measurements from a moving antenna. The forward map, derived from Maxwell’s equations, is inherently nonlinear, accounts for multiple scattering, and exhibits high-frequency oscillations that make traditional nonlinear least-squares formulations prone to local minima.
We present an alternative two-step approach centered on the construction of data-driven Reduced Order Models (ROMs). The first step computes a non-iterative map from the measurements to an approximation of the internal electric field. This internal wave is designed to fit the data by construction. The second step utilizes an iterative optimization to minimize the discrepancy between this internal field and the solution to the governing Maxwell's equations across all antenna locations.
While the ROM-based approach provides a superior estimate of the target support compared to standard SAR imaging, its performance is sensitive to the algebraic properties of the data-driven operators. In this talk, we focus on the linear algebraic challenges involved in stabilizing these ROMs. Specifically, we discuss the spectral properties of the data-driven mass and stiffness matrices and review regularization techniques to maintain robustness when the monostatic data is polluted with noise and preserve the structure of the ROM. Numerical simulations demonstrate that these stabilized ROMs allow for accurate quantitative estimation of the wave speed in regimes where standard inversion methods fail.