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

Yutong Du, Zicheng Liu, Yi Huang, Bazargul Matkerim, Bo Qi, Yali Zong, Peixian Han

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.

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

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.
Paper Structure (22 sections, 19 equations, 13 figures, 1 table)

This paper contains 22 sections, 19 equations, 13 figures, 1 table.

Table of Contents

  1. Introduction
  2. Physics-Based Formulation of the Inverse Scattering Problem
  3. Lippmann-Schwinger Integral Model
  4. Contraction Integral Equation Model
  5. Fourier Bases-Expansion
  6. Contrast-Compensated Operator
  7. Physics-Driven Fourier-Spectral Neural Network Solver
  8. Network architecture
  9. Loss Function
  10. Training settings
  11. Numerical Analysis
  12. Multi-Parameter Sensitivity Analysis: $\beta$, $M_F$, and $k$
  13. Robustness to Noise and Comparative Study
  14. Interplay between noise and model parameters
  15. Comparative analysis with baseline solvers
  16. ...and 7 more sections

Figures (13)

  • Figure 1: Schematic of the 2-D inverse scattering configuration.
  • Figure 2: Conceptual workflow of the contrast-compensated operator (CCO) demonstrating edge-restoration through self-guided projection.
  • Figure 3: Computational pipeline of the proposed PDF solver, divided into initialization, neural network optimization, and profile reconstruction.
  • Figure 4: The network architecture of the proposed solver, where the input consists of two channels representing the real and imaginary parts of the initial Fourier coefficients by the 2-D discrete Fourier transform.
  • Figure 5: A comprehensive parameter analysis by fixing $\beta$ and varying the iteration number $k$ and $M_F$.
  • ...and 8 more figures