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

arXiv: https://arxiv.org/abs/2509.11926 · HTML: https://mlsanity.com/paper/2509.11926/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Residual Feature Distillation Network for Lightweight Image Super-Resolution](https://mlsanity.com/paper/2009.11551/) (2020)
- [White-Box Transformers via Sparse Rate Reduction](https://mlsanity.com/paper/2306.01129/) (2023)
- [Spatially-Adaptive Feature Modulation for Efficient Image Super-Resolution](https://mlsanity.com/paper/2302.13800/) (2023)
- [Residual Local Feature Network for Efficient Super-Resolution](https://mlsanity.com/paper/2205.07514/) (2022)
- [Graph Spectral Image Processing](https://mlsanity.com/paper/1801.04749/) (2018)
- [Graph-Based Blind Image Deblurring From a Single Photograph](https://mlsanity.com/paper/1802.07929/) (2018)
- [Interpretable Lightweight Transformer via Unrolling of Learned Graph Smoothness Priors](https://mlsanity.com/paper/2406.04090/) (2024)
- [Mixed Graph Signal Analysis of Joint Image Denoising / Interpolation](https://mlsanity.com/paper/2309.10114/) (2023)

## Abstract (arXiv)

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.