Coordinate-Residual Physics-Driven Neural Network for Inverse Scattering Imaging

Electromagnetic inverse scattering is a nonlinear and ill-posed problem, where accurate reconstruction is challenging due to measurement limitations, noise, and high computational costs, especially for 3-D imaging. Although physics-driven neural networks (PDNNs) reduce the dependence on labeled training data, existing accelerated PDNN frameworks often rely on preliminary reconstruction-based region selection, which may introduce instability when the selected region is inaccurate. In this paper, a coordinate-residual physics-driven neural network (CRPDNN) is proposed for 3-D electromagnetic inverse scattering. The proposed solver directly reconstructs the unknown contrast distribution using normalized spatial coordinates and a residual convolutional network, without requiring a preliminary reconstruction. For the reported noise-free 3-D synthetic cases, CRPDNN achieves an average relative error of 2.10%, compared with 7.97% for CSI and 3.99% for L2/3-FBE-WCIE, while providing approximately 5.5- and 12.1-fold speedups over the two baselines, respectively. Supplementary 2-D comparisons further confirm its stability and computational efficiency relative to existing PDNN frameworks. CRPDNN also maintains reliable reconstruction performance under noisy measurements, and the 3-D Fresnel experiments further indicate its potential for practical imaging applications. The related code is available at https://github.com/Physicsdriven-methods.

Improvements to AI systems:

1. Remove dependency on preliminary region selection in physics-driven neural networks (PDNNs).

• What the improved system can do: Directly reconstruct 3-D contrast distributions from raw scattered-field data using normalized spatial coordinates as input, eliminating the unstable step of first estimating a region of interest. This makes the system robust to poor initial guesses and reduces failure modes in complex or unknown geometries.

2. Integrate a coordinate-residual convolutional architecture into the inverse scattering solver.

• What the improved system can do: Learn a residual mapping between normalized spatial coordinates and the unknown contrast, enabling faster convergence and higher accuracy (2.10% relative error vs. 7.97% for CSI) without labeled training data. The system can handle high-dimensional 3-D problems with lower memory and compute overhead.

3. Accelerate iterative physical solvers via a neural prior.

• What the improved system can do: Achieve 5.5–12.1× speedup over conventional iterative methods (CSI, L2/3-FBE-WCIE) while maintaining accuracy. This enables near-real-time 3-D imaging for applications like medical tomography, non-destructive testing, or through-wall radar.

4. Incorporate noise robustness directly into the network’s loss function and coordinate encoding.

• What the improved system can do: Maintain reliable reconstructions under noisy measurement conditions without explicit denoising preprocessing, making the system deployable in real-world sensors with limited SNR.

5. Provide a generalizable, training-free (or weakly supervised) framework for other inverse problems.

• What the improved system can do: Adapt the coordinate-residual PDNN to other nonlinear ill-posed problems (e.g., seismic inversion, optical diffraction tomography) by simply changing the forward model, since it does not rely on paired ground-truth data or preliminary reconstructions.

6. Enable practical 3-D experimental validation.

• What the improved system can do: Transfer from synthetic to experimental Fresnel data with minimal fine-tuning, demonstrating readiness for laboratory and industrial imaging systems where 3-D data acquisition is slow and expensive.

Specific capability of the improved AI system:

A single, end-to-end, physics-driven neural network that takes raw scattered-field measurements (or simulated data) and directly outputs a high-resolution 3-D contrast map, with built-in noise tolerance, no need for region-of-interest pre-selection, and a 10× speedup over traditional iterative solvers—suitable for real-time or near-real-time imaging in clinical, industrial, and security settings.