  Image restoration problems are typically ill-posed requiring the design of
suitable priors. These priors are typically hand-designed and are fully
instantiated throughout the process. In this paper, we introduce a novel
framework for handling inverse problems related to image restoration based on
elements from the half quadratic splitting method and proximal operators.
Modeling the proximal operator as a convolutional network, we defined an
implicit prior on the image space as a function class during training. This is
in contrast to the common practice in literature of having the prior to be
fixed and fully instantiated even during training stages. Further, we allow
this proximal operator to be tuned differently for each iteration which greatly
increases modeling capacity and allows us to reduce the number of iterations by
an order of magnitude as compared to other approaches. Our final network is an
end-to-end one whose run time matches the previous fastest algorithms while
outperforming them in recovery fidelity on two image restoration tasks. Indeed,
we find our approach achieves state-of-the-art results on benchmarks in image
denoising and image super resolution while recovering more complex and finer
details.
