Provably Contractive and High-Quality Denoisers for Convergent Restoration
Organizations: Indian Institute of Technology Madras, India
Abstract
Image restoration, the recovery of clean images from degraded measurements, has applications in various domains like surveillance, defense, and medical imaging. While modern convolutional and attention-based networks achieve strong restoration quality, they typically lack explicit stability guarantees under small input perturbations. In this work, we develop provably contractive denoiser networks with global Lipschitz constant smaller than one. Our design composes proximal layers obtained from unfolding techniques, with Lipschitz-controlled convolutional refinements. By contractivity, the proposed denoiser guarantees that input perturbations of strength induce at most change at the output, whereas strong unconstrained baselines such as DnCNN and Restormer can exhibit larger deviations under the same perturbations. On image denoising, our model substantially improves over prior provably 1-Lipschitz / contractive baselines and narrows the gap to strong unconstrained denoisers. In addition, when used as a prior in Plug-and-Play restoration, the proposed denoiser yields provable convergence and strong empirical performance. Overall, our results show that strict Lipschitz control need not preclude practically competitive restoration quality, and suggest that stable, verifiable restoration models can be achieved without a severe loss in performance. Codes and pretrained models are available at https://github.com/SHUBHI1553/Contractive-Denoisers
Figures & tables
| Method | CBSD68 | Kodak24 | Urban100 | ||||||
|---|---|---|---|---|---|---|---|---|---|
| eSN-ReLU | |||||||||
| eSN-GS | |||||||||
| D-FBS | |||||||||
| D-DRS | |||||||||
| Ours | |||||||||
| Method | BSD68 | Set12 | Urban100 | ||||||
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| eSN-ReLU | |||||||||
| eSN-GS | |||||||||
| D-FBS | |||||||||
| D-DRS | |||||||||
| Ours | |||||||||
| Dataset | PGD | DRS-Diff | GS | FBS | DRS |
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| CBSD68 | |||||
| Kodak24 | |||||
| Urban100 |
| Dataset | Diffusion-based PnP | PnP-FBS | |||||||
|---|---|---|---|---|---|---|---|---|---|
| DiffPIR | SGPnP | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | OURS | |
| CBSD68 | |||||||||
| Kodak24 | |||||||||
| Urban100 | |||||||||
| Dataset | Diffusion-based PnP | PnP-FBS | |||||||
|---|---|---|---|---|---|---|---|---|---|
| DiffPIR | SGPnP | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | OURS | |
| CBSD68 | |||||||||
| Kodak24 | |||||||||
| Urban100 | |||||||||
| Dataset | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | OURS |
|---|---|---|---|---|---|---|---|
| CBSD68 | |||||||
| Kodak24 | |||||||
| Urban100 |
| Dataset | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | OURS |
|---|---|---|---|---|---|---|---|
| CBSD68 | |||||||
| Kodak24 | |||||||
| Urban100 |
Appendix figures & tables30 assets
Supplementary material from the paper’s appendix.
Appendix
| Dataset, | -Lipschitz / Contractive Models | Unconstrained Models | Pretrained Models | ||||||
|---|---|---|---|---|---|---|---|---|---|
| D-FBS | D-DRS | Ours | IDF | DnCNN | Noise2VST | Restormer | CLIP | DIL | |
| CBSD68, | |||||||||
| CBSD68, | |||||||||
| CBSD68, | |||||||||
| Kodak24, | |||||||||
| Kodak24, | |||||||||
| Dataset, | -Lipschitz / Contractive Models | Unconstrained Models | Pretrained Models | |||||
|---|---|---|---|---|---|---|---|---|
| D-FBS | D-DRS | Ours | DnCNN | Restormer | MWCNN | CRR-NN ( -step) | CRR-NN (prox.) | |
| BSD68, | ||||||||
| BSD68, | ||||||||
| BSD68, | ||||||||
| Set12, | ||||||||
| Set12, | ||||||||
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | 26.26 | ||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | 22.76 | ||||||||||
| SSIM | 0.6896 |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | 24.24 | ||||||||||
| SSIM | 0.6219 | |||||||||||
| Kodak24 | PSNR | 25.08 | ||||||||||
| SSIM | 0.6491 | |||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM | 0.6134 |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRRNN( -step) | CRRNN(prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
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| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
| Dataset | Metric | FBS | DRS | IDF | Noise2VST | DnCNN | Restormer | CRR-NN ( -step) | CRR-NN (prox.) | MWCNN | CLIP | OURS |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CBSD68 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Kodak24 | PSNR | |||||||||||
| SSIM | ||||||||||||
| Urban100 | PSNR | |||||||||||
| SSIM |
Image Restoration
Image restoration uses computational methods to recover useful visual content from noisy, blurred, low-resolution, or otherwise degraded images.
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