Learning Integrodifferential Models for Image Denoising

We introduce an integrodifferential extension of the edge-enhancing anisotropic diffusion model for image denoising. By accumulating weighted structural information on multiple scales, our model is the first to create anisotropy through multiscale integration. It follows the philosophy of combining the advantages of model-based and data-driven approaches within compact, insightful, and mathematically well-founded models with improved performance. We explore trained results of scale-adaptive weighting and contrast parameters to obtain an explicit modelling by smooth functions. This leads to a transparent model with only three parameters, without significantly decreasing its denoising performance. Experiments demonstrate that it outperforms its diffusion-based predecessors. We show that both multiscale information and anisotropy are crucial for its success.