A Tunable Despeckling Neural Network Stabilized via Diffusion Equation

The removal of multiplicative Gamma noise is a critical research area in the application of synthetic aperture radar (SAR) imaging, where neural networks serve as a potent tool. However, real-world data often diverges from theoretical models, exhibiting various disturbances, which makes the neural network less effective. Adversarial attacks can be used as a criterion for judging the adaptability of neural networks to real data, since adversarial attacks can find the most extreme perturbations that make neural networks ineffective. In this work, the diffusion equation is designed as a regularization block to provide sufficient regularity to the whole neural network, due to its spontaneous dissipative nature. We propose a tunable, regularized neural network framework that unrolls a shallow denoising neural network block and a diffusion regularity block into a single network for end-to-end training. The linear heat equation, known for its inherent smoothness and low-pass filtering properties, is adopted as the diffusion regularization block. In our model, a single time step hyperparameter governs the smoothness of the outputs and can be adjusted dynamically, significantly enhancing flexibility. The stability and convergence of our model are theoretically proven. Experimental results demonstrate that the proposed model effectively eliminates high-frequency oscillations induced by adversarial attacks. Finally, the proposed model is benchmarked against several state-of-the-art denoising methods on simulated images, adversarial samples, and real SAR images, achieving superior performance in both quantitative and visual evaluations.