Graph Algorithm Unrolling with Douglas-Rachford Iterations for Image Interpolation with Guaranteed Initialization

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 the image interpolation problem and leveraging a recent theorem that maps a (pseudo-)linear interpolator Θ to a directed graph filter that is a solution to a MAP problem regularized with a graph shift variation (GSV) prior, we first initialize a directed graph adjacency matrix A based on a known interpolator Θ, 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 via Douglas-Rachford (DR) iterations, which we unroll into a lightweight interpretable neural net.Experimental results demonstrate state-of-the-art image interpolation results, while drastically reducing network parameters.