Proximal Splitting Networks for Image Restoration

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.