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Equivariant Plug-and-Play Image Reconstruction
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Shows that making plug-and-play, RED and ULA denoisers approximately equivariant via random group transformations at each iteration stabilizes image reconstruction and improves quality without retraining.
Problem
Plug-and-play (PnP), RED and Langevin algorithms that use implicit denoising priors are unstable and often diverge, hurting their versatility and reconstruction quality.
Approach
Enforce equivariance of any pretrained denoiser to rotations, reflections and translations by applying a randomly sampled group transformation to the denoiser input and its inverse to the output at each iteration (a Monte Carlo estimate of Reynolds averaging), with theory showing symmetric Jacobians and lower Lipschitz constants for linear denoisers.
Key results
- Equivariant DRUNet in PnP raises motion deblurring Set3C PSNR from 10.1 to 18.0 dB, and equivariant DnCNN reaches 30.7 vs 29.9 dB.
- Averaging over 90-degree rotations and reflections reduces DnCNN Jacobian asymmetry from 0.014 to 0.003 and DRUNet from 0.030 to 0.008.
- Equivariant denoisers reduce local Lipschitz constant of the PnP iteration for DRUNet from 0.83 to 0.70 on inpainting.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add random rotations and reflections to the DnCNN denoiser at each iteration (ablation) | PnP with DnCNN · MRI ×8 | PSNR: div. -> 24.6 ± 2.9 | Helped |
| Add random rotations and reflections to the DnCNN denoiser at each iteration (ablation) | PnP with DnCNN · Gaussian deblurring, Set3C | PSNR: 22.0 ± 6.0 -> 29.8 ± 3.1 | Helped |
| Add random rotations and reflections to the DnCNN denoiser at each iteration (ablation) | PnP with DnCNN · Motion deblurring, Set3C | PSNR: 29.9 ± 1.9 -> 30.7 ± 1.6 | Helped |
| Add random rotations and reflections to the DnCNN denoiser at each iteration (ablation) | PnP with DnCNN · Motion deblurring, BSD10 | PSNR: 30.4 ± 0.3 -> 30.9 ± 0.1 | Helped |
| Add random rotations and reflections to the DnCNN denoiser at each iteration (ablation) | PnP with DnCNN · Gaussian deblurring, BSD10 | PSNR: 29.6 ± 4.6 -> 33.0 ± 0.6 | Helped |
| Add random rotations and reflections to the DnCNN denoiser at each iteration (ablation) | PnP with DnCNN · MRI ×4 | PSNR: 28.6 ± 4.3 -> 30.1 ± 3.9 | Helped |
| Add random rotations and reflections to the DRUNet denoiser at each iteration (ablation) | PnP with DRUNet · Motion deblurring, BSD10 | PSNR: 16.5 ± 9.8 -> 28.4 ± 2.3 | Helped |
| Add random rotations and reflections to the DRUNet denoiser at each iteration (ablation) | PnP with DRUNet · Gaussian deblurring, Set3C | PSNR: 14.6 ± 8.8 -> 25.3 ± 10.1 | Helped |
| Add random rotations and reflections to the DRUNet denoiser at each iteration (ablation) | PnP with DRUNet · MRI ×4 | PSNR: 27.7 ± 4.0 -> 30.7 ± 3.0 | Helped |
| Add random rotations and reflections to the DRUNet denoiser at each iteration (ablation) | PnP with DRUNet · MRI ×8 | PSNR: 16.9 ± 8.6 -> 22.0 ± 6.0 | Helped |
| Add random rotations and reflections to the DRUNet denoiser at each iteration (ablation) | PnP with DRUNet · Motion deblurring, Set3C | PSNR: 10.1 ± 1.5 -> 18.0 ± 6.0 | Helped |
| Add random rotations and reflections to the DRUNet denoiser at each iteration (ablation) | PnP with DRUNet · Gaussian deblurring, BSD10 | PSNR: 17.5 ± 10.5 -> 31.9 ± 1.1 | Helped |
Surprising findings
- SCUNet and DiffUNet backbones still show artifacts or non-convergence even with equivariance, so the method does not always stabilize.
- Equivariant denoising does not clearly improve over non-equivariant SCUNet backbones.
Limitations
- Still prone to divergence and hallucinated artifacts with some backbones such as SCUNet and DRUNet after many iterations.
- Does not clearly improve over non-equivariant counterparts for SCUNet backbone.
Experimental setup
Datasets: Set3C BSD10 BSD68 fastMRI validation subset
Benchmarks: Set3C BSD10 MRI k-space validation subset
Metrics: PSNR relative Jacobian symmetry error local Lipschitz constant convergence criterion
Baselines: LipDnCNN GSPnP DPIR wavelets TGV
Builds on: plug-and-play priors regularization by denoising DPIR unadjusted Langevin algorithm
Closest papers by meaning
- Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction (NeurIPS 2024 · similarity 0.88)
- Plug-and-Play image restoration with Stochastic deNOising REgularization (ICML 2024 · similarity 0.87)
- A Regularization-Guided Equivariant Approach for Image Restoration (CVPR 2025 · similarity 0.86)
- PnP-Flow: Plug-and-Play Image Restoration with Flow Matching (ICLR 2025 · similarity 0.86)
- Learning Cocoercive Conservative Denoisers via Helmholtz Decomposition for Poisson Imaging Inverse Problems (NeurIPS 2025 · similarity 0.85)
- Adapt and Diffuse: Sample-adaptive Reconstruction via Latent Diffusion Models (ICML 2024 · similarity 0.85)
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