# Provably Contractive and High-Quality Denoisers for Convergent Restoration

arXiv: https://arxiv.org/abs/2603.26168 · HTML: https://mlsanity.com/paper/2603.26168/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 54 references that are in the map.
- First posted on arXiv 27 Mar 2026.

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

- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)
- [Orthogonal Convolutional Neural Networks](https://mlsanity.com/paper/1911.12207/) (2019)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [The Singular Values of Convolutional Layers](https://mlsanity.com/paper/1805.10408/) (2018)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024)
- [Algorithmic Guarantees for Inverse Imaging with Untrained Network Priors](https://mlsanity.com/paper/1906.08763/) (2019)
- [Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions](https://mlsanity.com/paper/2210.16222/) (2022)
- [Introducing Hann windows for reducing edge-effects in patch-based image segmentation](https://mlsanity.com/paper/1910.07831/) (2019)
- [Plug-and-Play image restoration with Stochastic deNOising REgularization](https://mlsanity.com/paper/2402.01779/) (2024)
- [1-Lipschitz Layers Compared: Memory, Speed, and Certifiable Robustness](https://mlsanity.com/paper/2311.16833/) (2023)
- [IDF: Iterative Dynamic Filtering Networks for Generalizable Image Denoising](https://mlsanity.com/paper/2508.19649/) (2025)
- [Averaged Deep Denoisers for Image Regularization](https://mlsanity.com/paper/2207.07321/) (2022)
- [Self-Calibrated Variance-Stabilizing Transformations for Real-World Image Denoising](https://mlsanity.com/paper/2407.17399/) (2024)
- [Learning Firmly Nonexpansive Operators](https://mlsanity.com/paper/2407.14156/) (2024)

## Abstract (arXiv)

Image restoration, the recovery of clean images from degraded measurements, has applications in various domains like surveillance, defense, and medical imaging. Despite achieving state-of-the-art (SOTA) restoration performance, existing convolutional and attention-based networks lack stability guarantees under minor shifts in input, exposing a robustness accuracy trade-off. We develop provably contractive (global Lipschitz < 1) denoiser networks that considerably reduce this gap. Our design composes proximal layers obtained from unfolding techniques, with Lipschitz-controlled convolutional refinements. By contractivity, our denoiser guarantees that input perturbations of strength |δ|≤varepsilon induce at most varepsilon change at the output, while strong baselines such as DnCNN and Restormer can exhibit larger deviations under the same perturbations. On image denoising, the proposed model is competitive with unconstrained SOTA denoisers, reporting the tightest gap for a provably 1-Lipschitz model and establishing that such gaps are indeed achievable by contractive denoisers. Moreover, the proposed denoisers act as strong regularizers for image restoration that provably effect convergence in Plug-and-Play algorithms. Our results show that enforcing strict Lipschitz control does not inherently degrade output quality, challenging a common assumption in the literature and moving the field toward verifiable and stable vision models. Codes and pretrained models are available at https://github.com/SHUBHI1553/Contractive-Denoisers