SAR-FAH: A Frequency-Adaptive Hybrid Network based on Neural ODEs for Structural-Preserving SAR Despeckling

Synthetic Aperture Radar (SAR) images are inherently degraded by speckle noise that severely limits their reliability in high-precision applications. As a signal-dependent multiplicative noise, speckle noise exhibits distinct statistical properties in homogeneous and heterogeneous regions of SAR images, which are spatially coupled. Nevertheless, existing deep learning despeckling methods operate directly in the spatial domain overlooking this statistical difference. It imposes a suboptimal trade-off between noise suppression and structure preservation, inevitably leading to artifacts, edge blurring, and texture distortion. To address these limitations, we propose a Frequency-Adaptive Hybrid model based on Neural Ordinary Differential Equations (NODEs) for SAR despeckling, termed SAR-FAH. It is a novel divide-and-conquer architecture that performs despeckling in the frequency domain to achieve improved structural preservation. We first fully decouple homogeneous and heterogeneous regions in the frequency domain via wavelet transform according to their local spatial characteristics and then revisit the statistical characteristics of speckle noise. Guided by the distinct properties of each sub-band, we design specialized sub-networks for frequency-specific restoration. Specifically, based on the smoothness of the low-frequency sub-band, the low-frequency denoising process is controlled by the module based on NODEs to ensure sufficient smoothness without artifacts, while the high-frequency sub-bands are processed by enhanced U-Net by incorporating deformable convolutions to better suppress noise and preserve edges and textures. Extensive experiments on both synthetic and real SAR images demonstrate that the proposed SAR-FAH outperforms the state-of-the-art methods both quantitatively and qualitatively.