Provably Contractive and High-Quality Denoisers for Convergent Restoration

TL;DR

This paper introduces provably contractive denoiser networks with Lipschitz control, ensuring stability and convergence in image restoration tasks without sacrificing performance, and provides theoretical guarantees and practical results.

Contribution

It develops Lipschitz-controlled denoisers using unfolding techniques, offering provable stability and competitive performance compared to state-of-the-art methods.

Findings

Contractive denoisers guarantee input perturbation bounds.

Proposed models are competitive with unconstrained SOTA denoisers.

Enforcing Lipschitz constraints does not degrade output quality.

Abstract

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 $\|\delta\|\le\varepsilon$ 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