# Unrolling Nonconvex Graph Total Variation for Image Denoising

arXiv: https://arxiv.org/abs/2506.02381 · HTML: https://mlsanity.com/paper/2506.02381/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 3 Jun 2025.

## Builds on (most cited first, 10 of 10)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [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)
- [Tutorial on Diffusion Models for Imaging and Vision](https://mlsanity.com/paper/2403.18103/) (2024)
- [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)
- [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)

## Abstract (arXiv)

Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the ℓ0-norm to promote sparse signal representation. Instead, we propose a new non-convex total variation term in a graph setting (NC-GTV), such that when combined with an ℓ2-norm fidelity term for denoising, leads to a convex objective with no extraneous local minima. We define NC-GTV using a new graph variant of the Huber function, interpretable as a Moreau envelope. The crux is the selection of a parameter a characterizing the graph Huber function that ensures overall objective convexity; we efficiently compute a via an adaptation of Gershgorin Circle Theorem (GCT). To minimize the convex objective, we design a linear-time algorithm based on Alternating Direction Method of Multipliers (ADMM) and unroll it into a lightweight feed-forward network for data-driven parameter learning. Experiments show that our method outperforms unrolled GTV and other representative image denoising schemes, while employing far fewer network parameters.