Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework to obtain simple but effective models for various image restoration problems. The proposed approach is based on the concept of nonlinear reaction diffusion, but we extend conventional nonlinear reaction diffusion models by highly parametrized linear filters as well as highly parametrized influence functions. In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are learned from training data through a loss based approach. We call this approach TNRD -- Trainable Nonlinear Reaction Diffusion. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets with respect to the tested applications. Our trained models retain the structural simplicity of diffusion models and take only a small number of steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast.
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