Adversarial Attack Priors-Based Nondivergence Diffusion Equation Model for SAR Speckle Removal

Multiplicative gamma noise poses a major challenge in synthetic aperture radar (SAR) imaging, severely degrading image quality and complicating downstream interpretation tasks. Although deep learning techniques have demonstrated remarkable denoising capabilities, their performance often deteriorates on real-world data due to deviations from idealized noise models and various environmental interferences. To address these limitations, we propose a novel speckle noise removal model, named AAP-NDE, based on a nondivergence diffusion equation guided by adversarial attack priors. By incorporating prior knowledge of potential adversarial perturbations, the model adaptively adjusts diffusion coefficients: larger coefficients are applied in homogeneous or heavily corrupted regions to suppress noise effectively, while smaller coefficients are employed near edges and fine structures to preserve critical image details. We theoretically establish the existence and uniqueness of the model solution, ensuring mathematical soundness. Extensive experiments on synthetic and real SAR images demonstrate that AAP-NDE achieves strong robustness against adversarial attacks, consistently outperforming state-of-the-art methods in both noise suppression and structure preservation. These results highlight the potential of AAP-NDE for reliable and practical SAR image processing in challenging scenarios.