Fast Physics-Driven Untrained Network for Highly Nonlinear Inverse Scattering Problems

TL;DR

This paper introduces a fast, physics-driven Fourier-spectral solver for nonlinear inverse scattering that significantly speeds up reconstruction, enabling real-time microwave imaging with high accuracy and robustness.

Contribution

It proposes a spectral-domain dimensionality reduction technique combined with novel operators and loss functions to accelerate inverse scattering reconstruction.

Findings

Achieves 100-fold speedup over existing UNNs.

Provides robust performance under noise and uncertainties.

Enables real-time microwave imaging applications.

Abstract

Untrained neural networks (UNNs) offer high-fidelity electromagnetic inverse scattering reconstruction but are computationally limited by high-dimensional spatial-domain optimization. We propose a Real-Time Physics-Driven Fourier-Spectral (PDF) solver that achieves sub-second reconstruction through spectral-domain dimensionality reduction. By expanding induced currents using a truncated Fourier basis, the optimization is confined to a compact low-frequency parameter space supported by scattering measurements. The solver integrates a contraction integral equation (CIE) to mitigate high-contrast nonlinearity and a contrast-compensated operator (CCO) to correct spectral-induced attenuation. Furthermore, a bridge-suppressing loss is formulated to enhance boundary sharpness between adjacent scatterers. Numerical and experimental results demonstrate a 100-fold speedup over state-of-the-art UNNs with robust performance under noise and antenna uncertainties, enabling real-time microwave imaging applications.