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A Restoration Network as an Implicit Prior
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Introduces Deep Restoration Priors (DRP), which uses a pre-trained MMSE restoration network (SwinIR super-resolution) as an implicit prior for inverse problems, with a convergence analysis to a stationary point of an implicit objective.
Problem
Solving imaging inverse problems (deblurring, super-resolution) with priors given by general pre-trained restoration networks rather than only denoisers, which lack theory and principled adaptation.
Approach
Generalizes denoiser-based plug-and-play priors to any MMSE restoration operator H-scaled: the restoration network R implicitly defines a regularizer h(x) = -tau sigma^2 log p(Hx) via a generalized Tweedie formula, and a proximal-gradient iteration with scaled proximal operator yields convergence to stationary points.
Key results
- On Gaussian deblurring (kernel std 1.6), DRP reaches 30.69 dB on Set3c versus 29.53 dB for DPIR.
- On 2x SISR with std 1.6 kernel, DRP reaches 29.26 dB on Set3c versus 28.18 dB for DPIR.
- Theory: iterates satisfy min gradient-norm bound of order 1/t under a step size gamma = mu/(alpha L).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DRP with a SwinIR restoration prior instead of the denoiser-prior baselines | Image deblurring · Gaussian blur std 1.6, Set3c | PSNR (dB): 29.78 -> 30.69 | Helped |
| Use DRP with a SwinIR restoration prior instead of the denoiser-prior baselines | Image deblurring · Gaussian blur std 2.0, CBSD68 | PSNR (dB): 27.52 -> 27.46 | Mixed |
| Use DRP with a SwinIR restoration prior instead of denoiser-prior baselines | SISR 2× · Set3c and CBSD68 | PSNR (dB): 28.18 -> 29.26; 27.97 -> 28.12 | Helped |
| Use DRP with a SwinIR restoration prior instead of denoiser-prior baselines | SISR 3× · CBSD68, second Gaussian blur kernel | PSNR (dB): 26.39 -> 26.60 | Helped |
| Use DRP with a SwinIR restoration prior instead of DPS | Human-face image deblurring · FFHQ validation sample images, two blur kernels | PSNR (dB): 29.61 -> 34.61; 28.80 -> 33.05 | Helped |
| Gradually reduce the prior downsampling factor q, using 3× then 2× priors (ablation) | DRP image deblurring · Set3c | PSNR | Helped |
| Use only a 3× prior rather than the prior-refinement strategy (ablation) | DRP image deblurring · Set3c | PSNR | Hurt |
| Use only a 2× prior rather than the prior-refinement strategy (ablation) | DRP image deblurring · Set3c | PSNR | Hurt |
| Apply bicubic-trained SwinIR directly instead of using it as a DRP prior (ablation) | SISR · Set3c, 2× | PSNR | Hurt |
| Use a restoration-prior SwinIR as a DRP prior instead of a denoiser prior | Image deblurring · Set3c and Set5, Gaussian blur std 1.6 | PSNR (dB): 29.53 -> 30.69; 32.38 -> 32.79 | Helped |
Surprising findings
- A bicubic SR network used as a prior, despite being trained for a mismatched degradation, achieves SOTA when wrapped in DRP for SISR with blur kernels.
- Gradually reducing the SR downsampling factor (prior refinement) improves quality, analogous to annealing the denoiser noise level in DPIR.
Limitations
- Performance is bounded by the quality of the pre-trained restoration model, which is self-supervised and may underperform task-specific supervised priors.
- Theory assumes the restoration network performs MMSE estimation, which does not hold for networks trained with l1 or SSIM losses.
- Theoretical results rely on assumptions such as a non-degenerate prior and Lipschitz gradient of h.
Experimental setup
Datasets: DIV2K Flickr2K Set3c Set5 CBSD68 McMaster FFHQ
Benchmarks: Set3c Set5 CBSD68 McMaster FFHQ validation sample images
Metrics: PSNR
Baselines: SD-RED PnP-ADMM IRCNN+ DPIR GS-PnP DPS
Builds on: plug-and-play priors regularization by denoising DPIR SwinIR Tweedie's formula
Closest papers by meaning
- Stochastic Deep Restoration Priors for Imaging Inverse Problems (ICML 2025 · similarity 0.93)
- FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems (CVPR 2025 · similarity 0.91)
- Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance (CVPR 2024 · similarity 0.90)
- Blind Image Restoration via Fast Diffusion Inversion (NeurIPS 2024 · similarity 0.89)
- Unleashing the Denoising Capability of Diffusion Prior for Solving Inverse Problems (NeurIPS 2024 · similarity 0.88)
- A Diffusion Model with State Estimation for Degradation-Blind Inverse Imaging (AAAI 2024 · similarity 0.88)
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