CR-DEQ-SAR: A Deep Equilibrium Sparse SAR Imaging Method for Compound Regularization

Synthetic aperture radar (SAR) is a microwave remote sensing technology offering all-weather, high-resolution imaging. The rising demand for high precision and real-time processing under complex conditions in resource-constrained environments has spurred interest in deep network-based SAR imaging, which combines traditional sparse SAR imaging methods with deep learning to optimize parameters and scene features while retaining physical model interpretability and enabling fast inference. However, the single regularization cannot entirely capture the features of complex observation scenes, and network architectures based on iterative unfolding often face memory and numerical precision constraints during training. In this article, we propose a deep equilibrium sparse SAR Imaging method for compound regularization, integrating sparse and implicit regularizations to better capture complex scene features. The deep equilibrium model (DEQ) serves as a novel deep network framework that directly computes fixed points using analytical methods, theoretically allowing for infinite forward iterations while maintaining constant memory requirements. This is particularly advantageous in memory-intensive SAR imaging applications. Finally, we validate the effectiveness and superiority of the proposed method through experiments on real SAR scenes. The experimental results show that the proposed method outperforms existing deep learning-based SAR imaging methods regarding reconstruction performance and memory usage.