Abstract
Physics-driven neural solvers can reconstruct strongly nonlinear inverse scattering scenes without supervised training, but their per-instance optimization over pixel-wise unknowns is computationally expensive. This letter presents a fast physics-driven Fourier-spectral solver for two-dimensional transverse-magnetic inverse scattering. The induced current is parameterized in a truncated Fourier basis, so that the reconstruction is carried out in a compact spectral space rather than on dense spatial grids. To improve robustness in high-contrast regimes, a contraction integral equation is incorporated into the physics-consistency model. In addition, a contrast-compensated operator is introduced to alleviate boundary attenuation caused by spectral truncation, and a bridge-suppressing loss is designed to reduce false connections between adjacent scatterers. A lightweight fully connected network, initialized from a back-propagation-based estimate, optimizes the spectral coefficients for each measurement instance. Numerical examples and Fresnel experimental data show that the proposed method preserves the main target topology and quantitative contrast with sub-second reconstruction time. Compared with representative spatial-domain physics-driven solvers, it achieves nearly two orders of magnitude acceleration while maintaining competitive reconstruction quality, which is promising for fast microwave imaging applications.