Toward Constrained Generative Adversarial Network Architecture for Precision Microwave Imaging

Abstract

The electromagnetic (EM) inverse scattering problem aims to reconstruct the shape, location, and material properties of an unknown domain from scattered field measurements, a task that is inherently ill-posed and nonlinear. Herein, a deep-learning-based framework for reconstructing randomly shaped 2-D dielectric objects was discussed using multi-frequency scattered electric field data. An adversarial autoencoder was trained to generate complex scatterer geometries from a Gaussian-constrained latent space, which was then integrated, along with dense layers and a forward neural network, into a cohesive inverse neural network. The reconstructed images were validated through the numerical forward model, addressing non-uniqueness. Test data revealed, the proposed inversion framework could achieve an average test loss of 0.58 and a mean structural similarity index measure (SSIM) of <inline-formula> <tex-math notation="LaTeX">$0.96\pm 0.01$ </tex-math></inline-formula>. To evaluate reconstruction fidelity on complex-valued profiles, normalized mean square error (NMSE) and peak signal-to-noise ratio (PSNR) were computed, yielding values of <inline-formula> <tex-math notation="LaTeX">$0.07 \pm 0.02$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$22.64 \pm 1.19$ </tex-math></inline-formula> dB, respectively. Spatial error mapping confirmed that pixel-level variations occurred exclusively at sharp geometric boundaries, with the background and core profile remaining accurately resolved. The framework further exhibited robustness to measurement noise, preserving accurate scatterer geometry across scattered-field SNR levels ranging from 25 dB down to 5 dB, with the mean relative error increasing from 0.135 to 0.333 over this range. To further assess generalization capability, the pretrained models on moderate contrast profiles were fine-tuned using a dataset with higher dielectric contrast, introducing stronger scattering effects and increased nonlinearity. Despite the increased complexity, the framework successfully reconstructed the overall geometry of dielectric objects with SSIM value of 0.94 and ±0.02 standard deviation. Once trained, the proposed approach could generate results instantaneously, with an average inference time of <inline-formula> <tex-math notation="LaTeX">$0.58 \pm 0.07$ </tex-math></inline-formula> ms per sample on an NVIDIA GTX 1080 Ti GPU, overcoming the slow convergence limitations inherent to conventional iterative solvers. This work contributes to both machine learning and EM imaging by offering a real-time quantitative imaging approach, thereby opening up new avenues for radio-frequency inverse imaging.