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

2025-09-15

AI Summary

To address the issues of poor local minima susceptibility and limited interpretability arising from random initialization in conventional deep neural networks (DNNs) for image interpolation, this paper proposes a learnable graph filtering framework grounded in the graph shift total variation (GSTV) prior. Methodologically, we first establish a theoretical mapping from pseudo-linear interpolation operators to directed graph filtering structures, enabling deterministic, performance-guaranteed initialization of the adjacency matrix. Subsequently, we unroll the Douglas–Rachford splitting algorithm into a lightweight, fully interpretable neural architecture. Our approach significantly reduces model parameter count while achieving state-of-the-art interpolation performance across multiple benchmark datasets. The contributions include: (i) a theoretically principled initialization strategy rooted in graph signal processing; (ii) an intrinsically interpretable network design derived from proximal optimization; and (iii) superior efficiency and accuracy trade-offs, jointly ensuring rigorous mathematical foundations, structural transparency, and computational efficacy.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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 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.

Problem

• Initializing graph networks with known interpolators to avoid poor local minima
• Learning perturbation matrices from data to enhance graph adjacency
• Unrolling Douglas-Rachford iterations into lightweight interpretable neural networks

Innovation

• Graph algorithm unrolling with Douglas-Rachford iterations
• Initialization using known interpolator for baseline performance
• Learning perturbation matrices to augment graph adjacency