# Untrained Graph Neural Networks for Denoising

arXiv: https://arxiv.org/abs/2109.11700 · HTML: https://mlsanity.com/paper/2109.11700/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 64 references that are in the map.
- First posted on arXiv 24 Sep 2021.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecasting](https://mlsanity.com/paper/1802.07007/) (2018)
- [Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity](https://mlsanity.com/paper/1602.05897/) (2016)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [GraphGAN: Graph Representation Learning with Generative Adversarial Nets](https://mlsanity.com/paper/1711.08267/) (2017)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [Zero-Shot Self-Supervised Learning for MRI Reconstruction](https://mlsanity.com/paper/2102.07737/) (2021)
- [Trend Filtering on Graphs](https://mlsanity.com/paper/1410.7690/) (2014)
- [Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators](https://mlsanity.com/paper/1910.14634/) (2019)
- [HodgeNet: Graph Neural Networks for Edge Data](https://mlsanity.com/paper/1912.02354/) (2019)
- [Discrete Signal Processing on Graphs: Sampling Theory](https://mlsanity.com/paper/1503.05432/) (2015)
- [Graph Unrolling Networks: Interpretable Neural Networks for Graph Signal Denoising](https://mlsanity.com/paper/2006.01301/) (2020)
- [Signal Processing on Directed Graphs](https://mlsanity.com/paper/2008.00586/) (2020)
- [Algorithms for Learning Graphs in Financial Markets](https://mlsanity.com/paper/2012.15410/) (2020)
- [Axiomatic Construction of Hierarchical Clustering in Asymmetric Networks](https://mlsanity.com/paper/1301.7724/) (2013)
- [Hierarchical Clustering of Asymmetric Networks](https://mlsanity.com/paper/1607.06294/) (2016)
- [Learning Graph Topological Features via GAN](https://mlsanity.com/paper/1709.03545/) (2017)

## Built on by (most cited first, 15 of 15)

- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Towards Data-centric Graph Machine Learning: Review and Outlook](https://mlsanity.com/paper/2309.10979/) (2023)
- [Redesigning graph filter-based GNNs to relax the homophily assumption](https://mlsanity.com/paper/2409.08676/) (2024)
- [Convolutional Learning on Directed Acyclic Graphs](https://mlsanity.com/paper/2405.03056/) (2024)
- [Robust Graph Neural Network based on Graph Denoising](https://mlsanity.com/paper/2312.06557/) (2023)
- [Efficient Learning of Balanced Signed Graphs via Iterative Linear Programming](https://mlsanity.com/paper/2409.07794/) (2024)
- [Multilinear Kernel Regression and Imputation via Manifold Learning](https://mlsanity.com/paper/2402.03648/) (2024)
- [A Unified View Between Tensor Hypergraph Neural Networks And Signal Denoising](https://mlsanity.com/paper/2309.08385/) (2023)
- [Directed Acyclic Graph Convolutional Networks](https://mlsanity.com/paper/2506.12218/) (2025)
- [RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problems](https://mlsanity.com/paper/2510.17396/) (2025)
- [Artifact-Robust Graph-Based Learning in Digital Pathology](https://mlsanity.com/paper/2310.18192/) (2023)
- [Adversary-Robust Graph-Based Learning of WSIs](https://mlsanity.com/paper/2403.14489/) (2024)
- [DIPLI: Deep Image Prior Lucky Imaging for Blind Astronomical Image Restoration](https://mlsanity.com/paper/2503.15984/) (2025)
- [Burger: Robust Graph Denoising-augmentation Fusion and Multi-semantic Modeling in Social Recommendation](https://mlsanity.com/paper/2505.06612/) (2025)
- [Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming](https://mlsanity.com/paper/2506.01826/) (2025)

## Abstract (arXiv)

A fundamental problem in signal processing is to denoise a signal. While there are many well-performing methods for denoising signals defined on regular supports, such as images defined on two-dimensional grids of pixels, many important classes of signals are defined over irregular domains such as graphs. This paper introduces two untrained graph neural network architectures for graph signal denoising, provides theoretical guarantees for their denoising capabilities in a simple setup, and numerically validates the theoretical results in more general scenarios. The two architectures differ on how they incorporate the information encoded in the graph, with one relying on graph convolutions and the other employing graph upsampling operators based on hierarchical clustering. Each architecture implements a different prior over the targeted signals. To numerically illustrate the validity of the theoretical results and to compare the performance of the proposed architectures with other denoising alternatives, we present several experimental results with real and synthetic datasets.