mlsanityData to 7 Oct 2026

Untrained Graph Neural Networks for Denoising

arXiv 2109.11700 ↗First posted 24 Sep 2021eess.SP cs.LGcited by 15

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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.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 32 of its 64 references that are in the map. First posted on arXiv 24 Sep 2021.

Builds on

32 of 64 references.

References · 32

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  4. 2017Modeling Relational Data with Graph Convolutional Networkscited by 1,684
  5. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
  6. 2017Deep Image Priorcited by 1,097
  7. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  8. 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
  9. 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 409
  10. 2018Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecastingcited by 145
  11. 2016Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivitycited by 138
  12. 2017Cooperative Game Theory Approaches for Network Partitioningcited by 134
20 more
  1. 2017GraphGAN: Graph Representation Learning with Generative Adversarial Netscited by 121
  2. 2018Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networkscited by 120
  3. 2018Convolutional Neural Network Architectures for Signals Supported on Graphscited by 94
  4. 2019DeepRED: Deep Image Prior Powered by REDcited by 84
  5. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 81
  6. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  7. 2013Discrete Signal Processing on Graphs: Frequency Analysiscited by 72
  8. 2021Zero-Shot Self-Supervised Learning for MRI Reconstructioncited by 53
  9. 2014Trend Filtering on Graphscited by 45
  10. 2019Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generatorscited by 40
  11. 2019HodgeNet: Graph Neural Networks for Edge Datacited by 39
  12. 2015Discrete Signal Processing on Graphs: Sampling Theorycited by 33
  13. 2020Graph Unrolling Networks: Interpretable Neural Networks for Graph Signal Denoisingcited by 33
  14. 2020Signal Processing on Directed Graphscited by 28
  15. 2020Algorithms for Learning Graphs in Financial Marketscited by 14
  16. 2013Axiomatic Construction of Hierarchical Clustering in Asymmetric Networkscited by 5
  17. 2016Hierarchical Clustering of Asymmetric Networkscited by 5
  18. 2017Learning Graph Topological Features via GANcited by 5
  19. 2019Blind identification of stochastic block models from dynamical observationscited by 5
  20. 2019An Underparametrized Deep Decoder Architecture for Graph Signalscited by 3

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Cited by year

Citing papers per year: 2022: 1; 2023: 4; 2024: 5; 2025: 5.

15 papers.

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  1. 2022Theoretical Perspectives on Deep Learning Methods in Inverse Problemscited by 22
  2. 2023Towards Data-centric Graph Machine Learning: Review and Outlookcited by 15
  3. 2024Redesigning graph filter-based GNNs to relax the homophily assumptioncited by 8
  4. 2024Convolutional Learning on Directed Acyclic Graphscited by 6
  5. 2024Efficient Learning of Balanced Signed Graphs via Iterative Linear Programmingcited by 4
  6. 2023Robust Graph Neural Network based on Graph Denoisingcited by 3
  7. 2024Multilinear Kernel Regression and Imputation via Manifold Learningcited by 3
  8. 2023A Unified View Between Tensor Hypergraph Neural Networks And Signal Denoisingcited by 1
  9. 2025Directed Acyclic Graph Convolutional Networkscited by 1
  10. 2025RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problemscited by 1
  11. 2023Artifact-Robust Graph-Based Learning in Digital Pathologycited by 0
  12. 2024Adversary-Robust Graph-Based Learning of WSIscited by 0
3 more
  1. 2025DIPLI: Deep Image Prior Lucky Imaging for Blind Astronomical Image Restorationcited by 0
  2. 2025Burger: Robust Graph Denoising-augmentation Fusion and Multi-semantic Modeling in Social Recommendationcited by 0
  3. 2025Efficient Learning of Balanced Signed Graphs via Sparse Linear Programmingcited by 0