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Stochastic Deep Restoration Priors for Imaging Inverse Problems
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Proposes ShaRP, an optimization framework that uses an ensemble of stochastically sampled deep restoration models (beyond Gaussian denoisers) as priors for imaging inverse problems, with a closed-form regularizer and self-supervised training from undersampled MRI.
Problem
Imaging inverse problems (CS-MRI and single-image super-resolution) rely on denoiser priors that only model Gaussian noise; restoration priors are underused and typically fixed to one degradation, and training denoisers requires fully sampled data.
Approach
Use a restoration network trained on a family of degradation operators as an ensemble of MMSE operators; each iteration samples a degradation H and takes a gradient step using the residual R(s,H) - x, which is an unbiased stochastic gradient of a regularizer defined as the expected negative log-likelihood of degraded observations.
Key results
- On 4x uniform CS-MRI at noise 0.005, ShaRP reaches 37.59 dB PSNR / 0.963 SSIM, above DRP (35.52) and DDS (35.21) though below retrained E2E-VarNet (38.10).
- With a self-supervised prior trained only on undersampled MRI, ShaRP reaches 33.87 dB PSNR at noise 0.005, outperforming SPICER (31.87) and GRAPPA (28.09).
- On ImageNet 2x SISR with blur sigma 1.25 noiseless, ShaRP attains 30.09 dB PSNR / 0.891 SSIM, the best PSNR and SSIM, while LPIPS ranks second behind DiffPIR-level perceptual results.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ShaRP with an ensemble of restoration priors instead of denoiser- and diffusion-based baselines | CS-MRI reconstruction · 4× uniform masks, σ = 0.005, 0.010, and 0.015 | PSNR: 37.59 vs 35.88; 35.81 vs 35.03; 34.92 vs 34.51 | Helped |
| Train the restoration prior self-supervisedly from incomplete measurements and use it in ShaRP | CS-MRI reconstruction · 4× uniform masks, σ = 0.005, 0.010, and 0.015 | PSNR: 33.87 vs 31.87; 33.64 vs 31.67; 33.21 vs 31.50 | Helped |
| Use ShaRP with a deblurring restoration prior instead of the compared denoiser- and diffusion-based methods | 2× SISR · ImageNet, two blur kernels and noiseless/noisy cases | PSNR: 30.09 vs 29.28; 29.03 vs 28.87; 29.28 vs 28.24; 28.06 vs 28.02 | Helped |
| Use an ensemble of restoration priors instead of a single fixed restoration prior (ablation) | ShaRP · CS-MRI | PSNR | Helped |
| Vary the number of restoration priors in the ensemble (ablation) | ShaRP · CS-MRI | PSNR | Mixed |
| Vary α, which controls prior selection (ablation) | ShaRP · CS-MRI | PSNR | Mixed |
| Use a pre-trained super-resolution prior for CS-MRI instead of the task-matched MRI restoration prior (ablation) | ShaRP · CS-MRI | PSNR | Mixed |
Surprising findings
- ShaRP using a self-supervised restoration prior trained only on undersampled MRI outperforms DPIR and DPS that use Gaussian denoisers trained on fully sampled images.
- ShaRP ranks second in LPIPS on SISR, indicating the optimization-based approach trades perceptual quality for distortion.
Limitations
- Optimization-based approach is limited in perceptual quality by the perception-distortion trade-off; no sampling-based extension yet.
- Supervised CS-MRI prior is fixed to alpha=0.5 subset at inference to simplify computation, and step size and regularization are tuned per setting on validation slices.
- E2E-VarNet, which is retrained per task, still outperforms ShaRP in CS-MRI.
Experimental setup
Datasets: fastMRI ImageNet
Benchmarks: fastMRI CS-MRI 4x and 6x uniform/random masks ImageNet SISR 2x with Gaussian blur (sigma 1.25, 1.5)
Metrics: PSNR SSIM LPIPS
Baselines: PnP-FISTA PnP-ADMM DPS DDS DRP TV GRAPPA SPICER DPIR DDNM DiffPIR DDRM
Builds on: Regularization by Denoising (RED) SNORE Deep Restoration Priors (DRP) InDI I2SB SSDEQ
Closest papers by meaning
- A Restoration Network as an Implicit Prior (ICLR 2024 · similarity 0.93)
- FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems (CVPR 2025 · similarity 0.89)
- RestoreGrad: Signal Restoration Using Conditional Denoising Diffusion Models with Jointly Learned Prior (ICML 2025 · similarity 0.88)
- Exact Posterior Score Estimation for Solving Linear Inverse Problems (NeurIPS 2026 · similarity 0.88)
- A Diffusion Model with State Estimation for Degradation-Blind Inverse Imaging (AAAI 2024 · similarity 0.88)
- Plug-and-Play image restoration with Stochastic deNOising REgularization (ICML 2024 · similarity 0.88)
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