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

• URL: http://arxiv.org/abs/2509.11926v2
• Date: Mon, 06 Oct 2025 15:13:53 GMT
• Title: Graph Algorithm Unrolling with Douglas-Rachford Iterations for Image Interpolation with Guaranteed Initialization
• Authors: Xue Zhang, Bingshuo Hu, Gene Cheung,
• Abstract summary: Conventional deep neural nets (DNNs) initialize network parameters at random and then optimize each one via descent, resulting in substantial risk of poor-performing local minima.<n>This paper presents a solution that maps a (pseudo-)linear interpolator Theta to a directed graph filter that is a solution to a MAP problem regularized with a graph shift variation (GSV) prior.<n>Experimental results demonstrate state-of-the-art image results, while drastically reducing network parameters.
• Score: 30.266182085126175
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 the image interpolation problem and leveraging a recent theorem that maps a (pseudo-)linear interpolator {\Theta} 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 {\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 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.

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