GAN-driven Electromagnetic Imaging of 2-D Dielectric Scatterers (2402.10831v1)

Abstract: Inverse scattering problems are inherently challenging, given the fact they are ill-posed and nonlinear. This paper presents a powerful deep learning-based approach that relies on generative adversarial networks to accurately and efficiently reconstruct randomly-shaped two-dimensional dielectric objects from amplitudes of multi-frequency scattered electric fields. An adversarial autoencoder (AAE) is trained to learn to generate the scatterer's geometry from a lower-dimensional latent representation constrained to adhere to the Gaussian distribution. A cohesive inverse neural network (INN) framework is set up comprising a sequence of appropriately designed dense layers, the already-trained generator as well as a separately trained forward neural network. The images reconstructed at the output of the inverse network are validated through comparison with outputs from the forward neural network, addressing the non-uniqueness challenge inherent to electromagnetic (EM) imaging problems. The trained INN demonstrates an enhanced robustness, evidenced by a mean binary cross-entropy (BCE) loss of $0.13$ and a structure similarity index (SSI) of $0.90$. The study not only demonstrates a significant reduction in computational load, but also marks a substantial improvement over traditional objective-function-based methods. It contributes both to the fields of machine learning and EM imaging by offering a real-time quantitative imaging approach. The results obtained with the simulated data, for both training and testing, yield promising results and may open new avenues for radio-frequency inverse imaging.

• The paper introduces a GAN-driven framework that reconstructs 2-D dielectric scatterers with a high SSIM of 0.97 and converged Binary Cross-Entropy loss of 0.01.
• It integrates an adversarial autoencoder with a forward neural network (MSE of 0.46×10⁻²) and an inverse neural network (test loss of 0.31×10⁻²) to tackle ill-posed EM inverse problems.
• The approach significantly reduces computational costs and sensitivity to noise, paving the way for real-time quantitative electromagnetic imaging.

GAN-driven Electromagnetic Imaging for 2-D Dielectric Scatterers: A Comprehensive Study

Introduction

Inverse scattering problems in electromagnetic (EM) imaging, characterized by their ill-posed and nonlinear nature, present substantial challenges that hamper the efficient reconstruction of two-dimensional dielectric objects. Traditional numerical methods for tackling these problems entail significant computational costs and can be particularly sensitive to measurement noise. The advent of deep learning (DL) techniques has paved the way for more effective and computationally efficient solutions to these complex forward and inverse scattering problems.

Literature Overview

Deep learning-driven electromagnetic (EM) imaging solutions are bifurcated into indirect and direct schemes. Indirect approaches rely on first leveraging simple models or auxiliary parameters, which are then refined or used to predict inverse parameters through more complex algorithms or pretrained neural networks that act as surrogate models, thereby reducing computational burdens. Direct methods, on the other hand, employ deep learning to infer material properties directly from measured scattered fields, despite the computational intensity and challenges posed by the EM inverse problem's inherent ill-posed nature.

Problem Formulation

The manuscript articulates the problem of accurately and efficiently reconstructing 2-D dielectric scatterers using multi-frequency scattered electric fields. It focuses on leveraging generative adversarial networks (GANs) to alleviate the extensive computational load traditionally associated with iterative numerical solvers in EM imaging. The proposed framework encompasses an adversarial autoencoder (AAE) designed to generate the scatterer’s geometry from a latent representation, thereby facilitating a real-time quantitative imaging approach.

Generative Deep Learning Framework

The proposed framework integrates three distinct deep learning models to address the problem at hand:

• Adversarial Autoencoder (AAE): Trained to generate 2-D dielectric scatterers from a latent space constrained to a Gaussian distribution. The AAE architecture embodies encoder, generator, and discriminator components, optimized through Binary Cross-Entropy loss and adversarial learning to ensure the encoder faithfully maps input geometries to a meaningful latent space, which the generator then uses to recreate the input geometries.
• Forward Neural Network (FNN): A CNN-based regression model tasked with establishing a relationship between 2-D dielectric objects and their corresponding scattered electric fields at specified frequencies. The FNN employs Mean Squared Error (MSE) as a loss function, alongside L2 regularization, to combat overfitting while ensuring effective learning.
• Inverse Neural Network (INN): This network amalgamates initially untrained dense layers with the pretrained generator from the AAE, alongside a separately trained FNN. The INN utilizes a combination of reconstruction loss and Kullback-Leibler (KL) divergence for optimization, aiming to mitigate the non-uniqueness problem inherent in inverse EM imaging.

Numerical Results and Discussion

• The AAE demonstrated commendable performance, characterized by a convergence of the Binary Cross-Entropy loss to a mean value of 0.01 and a mean Structure Similarity Index of 0.97, indicating high fidelity in geometry generation.
• The FNN achieved an optimal test performance with an average MSE of 0.46×10^−2, affirming its capability to accurately model the relationship between 2-D dielectric profiles and scattered electric fields.
• For the INN, a reduction in test loss to 0.31×10^−2 was observed, with the mean Structure Similarity Index indicating a strong correlation between predicted and actual geometries.

Conclusion

This paper posits a significant advancement in the domain of electromagnetic imaging, demonstrating the efficacy of a generative deep learning approach in resolving the inverse scattering problem for 2-D dielectric scatterers. By integrating adversarial autoencoding principles with forward and inverse neural network architectures, the framework addresses the critical challenges of nonlinearity, ill-posedness, and computational inefficiency typically associated with traditional numerical methods. The promising results obtained highlight the potential of deep learning techniques in furthering the capabilities of real-time quantitative EM imaging, opening avenues for future developments in the field.

References

This section succinctly lists key references, underscoring the paper's grounding in both foundational and recent advances in electromagnetic imaging, deep learning, and generative models.