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Plug-and-Play image restoration with Stochastic deNOising REgularization
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Proposes SNORE, a stochastic plug-and-play regularization that applies the denoiser to noisy iterates at the matching noise level, solved via SGD with an annealed variant, and shows competitive deblurring and inpainting results.
Problem
Plug-and-Play (PnP) and RED methods apply a denoiser to images whose noise decreases along iterations, unlike diffusion-based solvers that denoise re-noised images; this mismatch with denoiser training distribution and lack of a clean probabilistic interpretation motivates a new regularization for i
Approach
Define an explicit stochastic regularization R_sigma(x) = -E_{x~ p_sigma(x~|x)}[log p_sigma(x~)] whose gradient applies the MMSE denoiser to noise-injected iterates, yielding a stochastic gradient descent PnP scheme with convergence guarantees and an annealed variant over decreasing sigma.
Key results
- On CBSD10 deblurring at 5/255 noise, Ann-SNORE reaches 29.92 PSNR and 0.17 LPIPS versus RED Prox 30.64 PSNR and 0.15 LPIPS.
- On CBSD68 inpainting with p=0.5 masked pixels, Ann-SNORE Prox achieves 31.94 PSNR and 0.93 SSIM, the best distortion scores, and 0.04 LPIPS.
- Ann-SNORE gives better perceptual scores (LPIPS, BRISQUE) than RED Prox on deblurring, but is slower than competing deblurring methods due to many annealing levels.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use Ann-SNORE instead of RED Prox | CBSD10 deblurring · CBSD10 deblurring, 5/255 | PSNR: 30.64 -> 29.92 | Hurt |
| use Ann-SNORE instead of RED Prox | CBSD10 deblurring · CBSD10 deblurring, 10/255 | PSNR: 28.50 -> 27.91 | Hurt |
| use Ann-SNORE instead of RED Prox | CBSD10 deblurring · CBSD10 deblurring, 20/255 | LPIPS: 0.31 -> 0.32 | Helped |
| use Ann-SNORE instead of RED Prox | CBSD10 deblurring · CBSD10 deblurring, 20/255 | BRISQUE: 55.48 -> 28.88 | Hurt |
| use a proximal step on data fidelity (ablation) | Ann-SNORE · CBSD68 inpainting, random mask p=0.5 | PSNR: 31.65 -> 31.94 | Helped |
| use a proximal step on data fidelity (ablation) | Ann-SNORE · CBSD68 inpainting, random mask p=0.5 | BRISQUE: 7.10 -> 8.35 | Hurt |
| use Ann-SNORE instead of RED | CBSD68 inpainting · CBSD68 inpainting, random mask p=0.5 | PSNR: 31.26 -> 31.65 | Helped |
| use Ann-SNORE instead of RED | CBSD68 inpainting · CBSD68 inpainting, random mask p=0.5 | LPIPS: 0.07 -> 0.04 | Helped |
Surprising findings
- On deblurring, RED Prox has higher PSNR but much worse BRISQUE than Ann-SNORE, showing distortion and perceptual metrics disagree.
- DiffPIR does not outperform in deblurring because the denoiser is not trained for highly noisy images.
Limitations
- Ann-SNORE is computationally more expensive for deblurring due to many annealing levels and iterations.
- Theoretical convergence assumes bounded iterates and a denoiser assumption that is hard to verify for learned denoisers.
- Experiments are limited to deblurring and inpainting on CBSD images with a single denoiser.
Experimental setup
Datasets: CBSD68 CBSD10
Benchmarks: CBSD10 deblurring CBSD68 inpainting
Metrics: PSNR SSIM LPIPS BRISQUE
Baselines: RED RED Prox DiffPIR PnP SGD
Builds on: Regularization by Denoising (RED) Plug-and-Play priors Gradient-Step denoiser DiffPIR PnP SGD
Closest papers by meaning
- Reconciling Stochastic and Deterministic Strategies for Zero-shot Image Restoration using Diffusion Model in Dual (CVPR 2025 · similarity 0.90)
- PnP-Flow: Plug-and-Play Image Restoration with Flow Matching (ICLR 2025 · similarity 0.90)
- Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction (NeurIPS 2024 · similarity 0.88)
- Learning Cocoercive Conservative Denoisers via Helmholtz Decomposition for Poisson Imaging Inverse Problems (NeurIPS 2025 · similarity 0.88)
- Stochastic Deep Restoration Priors for Imaging Inverse Problems (ICML 2025 · similarity 0.88)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.87)
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