# Deep Graph Laplacian Regularization for Robust Denoising of Real Images

arXiv: https://arxiv.org/abs/1807.11637 · HTML: https://mlsanity.com/paper/1807.11637/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2018.

## Built on by (most cited first, 13 of 13)

- [Graph Anomaly Detection in Time Series: A Survey](https://mlsanity.com/paper/2302.00058/) (2023)
- [Mask-GVAE: Blind Denoising Graphs via Partition](https://mlsanity.com/paper/2102.04228/) (2021)
- [Interpretable Lightweight Transformer via Unrolling of Learned Graph Smoothness Priors](https://mlsanity.com/paper/2406.04090/) (2024)
- [DEALing with Image Reconstruction: Deep Attentive Least Squares](https://mlsanity.com/paper/2502.04079/) (2025)
- [LOCATEdit: Graph Laplacian Optimized Cross Attention for Localized Text-Guided Image Editing](https://mlsanity.com/paper/2503.21541/) (2025)
- [Graph-Based Depth Denoising & Dequantization for Point Cloud Enhancement](https://mlsanity.com/paper/2111.04946/) (2021)
- [Consistent Time-of-Flight Depth Denoising via Graph-Informed Geometric Attention](https://mlsanity.com/paper/2506.23542/) (2025)
- [Spectral Gap Regularization of Neural Networks](https://mlsanity.com/paper/2304.03096/) (2023)
- [Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer](https://mlsanity.com/paper/2409.06676/) (2024)
- [Unrolling Nonconvex Graph Total Variation for Image Denoising](https://mlsanity.com/paper/2506.02381/) (2025)
- [Parameter-Efficient CT Reconstruction via Deep Graph Laplacian Regularization](https://mlsanity.com/paper/2605.25348/) (2026)
- [Low-rank Updates in Slowly Time-varying Graphs for Spatial-Temporal Signal Interpolation](https://mlsanity.com/paper/2606.24011/) (2026)
- [Geometric 2D Scene Graph Generation](https://mlsanity.com/paper/2607.22325/) (2026)

## Abstract (arXiv)

Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image noise. In this work, we combine the robustness merit of model-based approaches and the learning power of data-driven approaches for real image denoising. Specifically, by integrating graph Laplacian regularization as a trainable module into a deep learning framework, we are less susceptible to overfitting than pure CNN-based approaches, achieving higher robustness to small datasets and cross-domain denoising. First, a sparse neighborhood graph is built from the output of a convolutional neural network (CNN). Then the image is restored by solving an unconstrained quadratic programming problem, using a corresponding graph Laplacian regularizer as a prior term. The proposed restoration pipeline is fully differentiable and hence can be end-to-end trained. Experimental results demonstrate that our work is less prone to overfitting given small training data. It is also endowed with strong cross-domain generalization power, outperforming the state-of-the-art approaches by a remarkable margin.