  Image restoration is a long-standing problem in low-level computer vision
with many interesting applications. We describe a flexible learning framework
based on the concept of nonlinear reaction diffusion models for various image
restoration problems. By embodying recent improvements in nonlinear diffusion
models, we propose a dynamic nonlinear reaction diffusion model with
time-dependent parameters (\ie, linear filters and influence functions). In
contrast to previous nonlinear diffusion models, all the parameters, including
the filters and the influence functions, are simultaneously learned from
training data through a loss based approach. We call this approach TNRD --
\textit{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 for the
tested applications. Our trained models preserve the structural simplicity of
diffusion models and take only a small number of diffusion steps, thus are
highly efficient. Moreover, they are also well-suited for parallel computation
on GPUs, which makes the inference procedure extremely fast.
