Unrolling Graph-based Douglas-Rachford Algorithm for Image Interpolation with Informed Initialization

Abstract

Conventional deep neural nets (DNNs) initialize network parameters at random and then optimize each one via stochastic gradient descent (SGD), resulting in substantial risk of poor-performing local minima. Focusing on image interpolation and leveraging a recent theorem that maps a (pseudo-)linear interpolator {\Theta} to a directed graph filter that is a solution to a corresponding MAP problem with a graph shift variation (GSV) prior, we first initialize a directed graph adjacency matrix A given a known interpolator {\Theta}, establishing a baseline performance. Then, towards further gain, we learn perturbation matrices P and P(2) from data to augment A, whose restoration effects are implemented progressively via Douglas-Rachford (DR) iterations, which we unroll into a lightweight and interpretable neural net. Experiments on different image interpolation scenarios demonstrate state-of-the-art performance, while drastically reducing network parameters and inference complexity.