$\Phi$-GAN: Physics-Inspired GAN for Generating SAR Images Under Limited Data

Approaches for improving generative adversarial networks (GANs) training under a few samples have been explored for natural images. However, these methods have limited effectiveness for synthetic aperture radar (SAR) images, as they do not account for the unique electromagnetic scattering properties of SAR. To remedy this, we propose a physics-inspired regularization method dubbed $\Phi-G A N$, which incorporates the ideal point scattering center (PSC) model of SAR with two physical consistency losses. The PSC model approximates SAR targets using physical parameters, ensuring that $\Phi-G A N$ generates SAR images consistent with real physical properties while preventing discriminator overfitting by focusing on PSC-based decision cues. To embed the PSC model into GANs for end-to-end training, we introduce a physics-inspired neural module capable of estimating physical parameters of SAR targets efficiently. This module retains the interpretability of the physical model and can be trained with limited data. We propose two physical loss functions: one for the generator, guiding it to produce SAR images with physical parameters consistent with real ones, and one for the discriminator, enhancing its robustness by basing decisions on PSC attributes. We evaluate $\Phi$-GAN across several conditional GAN (cGAN) models, demonstrating state-of-the-art performance in data-scarce scenarios on three SAR image datasets.