  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.
