# Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer

arXiv: https://arxiv.org/abs/2409.06676 · HTML: https://mlsanity.com/paper/2409.06676/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [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)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [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)
- [Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain](https://mlsanity.com/paper/1604.07948/) (2016)
- [Signed Graph Metric Learning via Gershgorin Disc Perfect Alignment](https://mlsanity.com/paper/2006.08816/) (2020)
- [Deep Graph Laplacian Regularization for Robust Denoising of Real Images](https://mlsanity.com/paper/1807.11637/) (2018)
- [Random Walk Graph Laplacian based Smoothness Prior for Soft Decoding of JPEG Images](https://mlsanity.com/paper/1607.01895/) (2016)
- [Unrolling of Deep Graph Total Variation for Image Denoising](https://mlsanity.com/paper/2010.11290/) (2020)
- [Bilateral Filter: Graph Spectral Interpretation and Extensions](https://mlsanity.com/paper/1303.2685/) (2013)
- [Blind estimation of white Gaussian noise variance in highly textured images](https://mlsanity.com/paper/1711.10792/) (2017)
- [Fast & Robust Image Interpolation using Gradient Graph Laplacian Regularizer](https://mlsanity.com/paper/2101.09951/) (2021)
- [Volumetric Attribute Compression for 3D Point Clouds using Feedforward Network with Geometric Attention](https://mlsanity.com/paper/2304.00335/) (2023)
- [Mixed Graph Signal Analysis of Joint Image Denoising / Interpolation](https://mlsanity.com/paper/2309.10114/) (2023)
- [Retinex-based Image Denoising / Contrast Enhancement using Gradient Graph Laplacian Regularizer](https://mlsanity.com/paper/2307.02625/) (2023)

## Abstract (arXiv)

An image denoiser can be used for a wide range of restoration problems via the Plug-and-Play (PnP) architecture. In this paper, we propose a general framework to build an interpretable graph-based deep denoiser (GDD) by unrolling a solution to a maximum a posteriori (MAP) problem equipped with a graph Laplacian regularizer (GLR) as signal prior. Leveraging a recent theorem showing that any (pseudo-)linear denoiser boldsymbol Psi, under mild conditions, can be mapped to a solution of a MAP denoising problem regularized using GLR, we first initialize a graph Laplacian matrix mathbf L via truncated Taylor Series Expansion (TSE) of boldsymbol Psi-1. Then, we compute the MAP linear system solution by unrolling iterations of the conjugate gradient (CG) algorithm into a sequence of neural layers as a feed-forward network -- one that is amenable to parameter tuning. The resulting GDD network is "graph-interpretable", low in parameter count, and easy to initialize thanks to mathbf L derived from a known well-performing denoiser boldsymbol Psi. Experimental results show that GDD achieves competitive image denoising performance compared to competitors, but employing far fewer parameters, and is more robust to covariate shift.