GAN-driven Electromagnetic Imaging of 2-D Dielectric Scatterers

TL;DR

The paper tackles the challenge of solving ill-posed, nonlinear EM inverse scattering problems for 2-D dielectric scatterers. It proposes a GAN-inspired framework with an adversarial autoencoder (AAE) to learn a Gaussian-constrained latent representation of scatterers, and an inverse neural network (INN) that uses a forward model to enforce a unique mapping from measured multi-frequency scattered fields to object geometry. A forward neural network (FNN) serves as a physics-based validator, ensuring the generated designs produce consistent scattering responses. On simulated data across four frequencies, the INN achieves a mean BCE of 0.13 and a structure similarity index (SSI) of 0.90, demonstrating robust, real-time inverse imaging with reduced computational burden compared to traditional optimization-based methods.

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.

Figures (9)

• Figure 1: Description of the 2-D EM imaging problem. Tx (Red) and Rx (Black) represents the transmitters, and receivers respectively. There are 8 Tx and 16 Rx used in the numerical simulations.
• Figure 2: Architecture of the adversarial autoencoder (AAE) designed for generating the structure of physical object by learning a predefined distribution. In the encoder phase, both the variance ($\sigma$) and mean ($\mu$) of the specified distribution are generated, and these parameters are subsequently re-parameterized to produce the latent space ($\hat{z}$). The generator part then utilizes $\hat{z}$ to reconstruct the original image. Simultaneously, the discriminator is trained to distinguish between samples drawn from the predefined distribution, $z$, and those generated by the model, $\hat{z}$.
• Figure 3: Architecture of the forward neural network (FNN), illustrating the spatial dimensions where the $z$-axis and $y$-axis represent the height and width of each layer, respectively. The $x$-axis corresponds to the number of channels in the corresponding layer.
• Figure 4: Schematic representation of complete architecture employed in developing the inverse neural network (INN). The INN integrates a dense layer block with a trained generator, forming a cohesive framework for inverse design. Trained FNN is only employed to facilitate the unique solution corresponding to scattered field. A combination of reconstruction loss and KL divergence is utilized for effective optimization of the model.
• Figure 5: Training and testing results of adversarial autoencoder (AAE). (a) Binary Cross Entropy (BCE) loss curve, illustrating the gradual and smooth convergence of the loss over successive epochs. (b) BCE loss curve representing the learning progress of discriminator over epochs. The fluctuations in the graph are attributed to adversarial learning, and ideally, it should remain close to $0.5$. (c) & (d) Display scatter plots illustrating BCE loss and Structure Similarity Index (SSI) computed across the entire test dataset, comprising $2000$ images. The mean BCE value is observed to converge around $0.01$, while mean SSI remains around $0.97$. (e) & (h) showcase the comparison of two randomly selected test images and corresponding generated images by AAE.