  For several decades, image restoration remains an active research topic in
low-level computer vision and hence new approaches are constantly emerging.
However, many recently proposed algorithms achieve state-of-the-art performance
only at the expense of very high computation time, which clearly limits their
practical relevance. In this work, we propose a simple but effective approach
with both high computational efficiency and high restoration quality. We extend
conventional nonlinear reaction diffusion models by several parametrized linear
filters as well as several parametrized influence functions. We propose to
train the parameters of the filters and the influence functions through a loss
based approach. Experiments show that our trained nonlinear reaction diffusion
models largely benefit from the training of the parameters and finally lead to
the best reported performance on common test datasets for image restoration.
Due to their structural simplicity, our trained models are highly efficient and
are also well-suited for parallel computation on GPUs.
