Douglas-Rachford Networks: Learning Both the Image Prior and Data Fidelity Terms for Blind Image Deconvolution

Blind deconvolution problems are heavily ill-posed where the specific blurring kernel is not known. Recovering these images typically requires estimates of the kernel. In this paper, we present a method called Dr-Net, which does not require any such estimate and is further able to invert the effects of the blurring in blind image recovery tasks. These image recovery problems typically have two terms, the data fidelity term (for faithful reconstruction) and the image prior (for realistic looking reconstructions). We use the Douglas-Rachford iterations to solve this problem since it is a more generally applicable optimization procedure than methods such as the proximal gradient descent algorithm. Two proximal operators originate from these iterations, one for the data fidelity term and the second for the image prior. It is non-trivial to design a hand-crafted function to represent these proximal operators which would work with real-world image distributions. We therefore approximate both these proximal operators using deep networks. This provides a sound motivation for the final architecture for Dr-Net which we find outperforms the state-of-the-art on two mainstream blind deconvolution benchmarks. While doing so, we also find that Dr-Net is one of the fastest algorithms according to wall-clock times.