Imaging Interiors: An Implicit Solution to Electromagnetic Inverse Scattering Problems

TL;DR

This paper tackles Electromagnetic Inverse Scattering Problems (EISP) by reframing the task as forward estimation through implicit neural representations (INRs). It introduces two MLPs to continuously model the relative permittivity $\varepsilon_r$ and the induced current $J$, enabling a physics-consistent forward pass that avoids explicit inverse estimation. By employing random spatial sampling and a joint data/state loss (plus total variation regularization), the method achieves high-resolution reconstructions with robustness to sparse data and noise, outperforming traditional and deep-learning baselines on synthetic and real-world benchmarks. The approach extends naturally to 3D imaging and offers flexible resolution, making it practical for diverse EISP applications while maintaining computational efficiency through forward-only optimization.

Abstract

Electromagnetic Inverse Scattering Problems (EISP) have gained wide applications in computational imaging. By solving EISP, the internal relative permittivity of the scatterer can be non-invasively determined based on the scattered electromagnetic fields. Despite previous efforts to address EISP, achieving better solutions to this problem has remained elusive, due to the challenges posed by inversion and discretization. This paper tackles those challenges in EISP via an implicit approach. By representing the scatterer's relative permittivity as a continuous implicit representation, our method is able to address the low-resolution problems arising from discretization. Further, optimizing this implicit representation within a forward framework allows us to conveniently circumvent the challenges posed by inverse estimation. Our approach outperforms existing methods on standard benchmark datasets. Project page: https://luo-ziyuan.github.io/Imaging-Interiors

Figures (17)

• Figure 1: The results of a standard test case belkebir1996usingwei2018deep in EISP. In an EISP system, the scatterer in the enclosed space $D$ is first illuminated by incoming electromagnetic waves emitted by transmitters and generates scattered fields. Then, the scattered fields measured by receivers are used to determine the scatterer's relative permittivity. We show results obtained by our method, BP belkebir2005superresolution, Twofold SOM zhong2009twofold, Gs SOM chen2009subspace, BPS wei2018deep, CS-Net sanghvi2019embedding, Physics-Net liu2022physics, and PGAN 9468919. The pixel values in the images indicate the values of the relative permittivity. RRMSE/SSIM values are shown below each figure.
• Figure 2: Overview of our implicit method. Two MLPs, $F_\theta$ and $H_\phi$, are used to implicitly represent relative permittivity $\varepsilon_r$ and induced current $J$, respectively. Random sampling is applied for comprehensive optimization. The predicted induced current $\hat{\mathbf{J}}$ is calculated by \ref{['eq:J']} based on relative permittivity $\varepsilon_r$ queried from $F_\theta$ and induced current $J$ directly queried from $H_\phi$. Then the state loss $\mathcal{L}_{\text{state}}$ is calculated by comparing the predicted $\hat{\mathbf{J}}$ and directly queried $\mathbf{J}$. Besides, the directly queried induced current $\mathbf{J}$ is used to compute the scattered fields $\hat{\mathbf{E}}^{\text{s}}$ by \ref{['eq:E']}. Data loss function $\mathcal{L}_{\text{data}}$ is constructed to evaluate the difference between predicted scattered fields $\hat{\mathbf{E}}^{\text{s}}$ and the measured values $\mathbf{E}^{\text{s}}$.
• Figure 3: Samples obtained from synthetic Circular-cylinder dataset and MNIST dataset. From left to right: ground truth, results obtained using our method, BP belkebir2005superresolution, Twofold SOM zhong2009twofold, Gs SOM chen2009subspace, BPS wei2018deep, CS-Net sanghvi2019embedding, Physics-Net liu2022physics, and PGAN 9468919. The pixel values in the images indicate the values of the relative permittivity. RRMSE/SSIM values are shown below each figure. The first row is a standard test case belkebir1996usingwei2018deep, a well-known pattern for the evaluation of EISP methods.
• Figure 4: Samples obtained from real-world Institut Fresnel’s database. From left to right: ground truth, results obtained using our method, BP belkebir2005superresolution, Twofold SOM zhong2009twofold, Gs SOM chen2009subspace, BPS wei2018deep, CS-Net sanghvi2019embedding, Physics-Net liu2022physics, and PGAN 9468919. The pixel values in the images indicate the values of the relative permittivity. RRMSE/SSIM values are shown below each figure.
• Figure 5: Samples obtained under $5\%$ and $30\%$ noise levels. From left to right: ground truth, results obtained using our method, BP belkebir2005superresolution, Twofold SOM zhong2009twofold, Gs SOM chen2009subspace, BPS wei2018deep, CS-Net sanghvi2019embedding, Physics-Net liu2022physics, and PGAN 9468919. The pixel values in the images indicate the values of the relative permittivity. RRMSE/SSIM values are shown below each figure.