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Generalized Recorrupted-to-Recorrupted: Self-Supervised Learning Beyond Gaussian Noise
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Extends self-supervised Recorrupted-to-Recorrupted (R2R) to non-Gaussian additive noise and natural exponential family noise (Poisson, Gamma, Binomial) by generating independent noisy pairs, yielding an unbiased supervised-equivalent MSE/NLL loss that recovers SURE as a special case.
Problem
Self-supervised image restoration from noisy measurements alone is well established for Gaussian noise (R2R, SURE), but its effectiveness for non-Gaussian additive noise and exponential-family noise such as Poisson and Gamma is unexplored.
Approach
Recorrupt each noisy measurement into two conditionally independent noisy versions via a noise-distribution-specific splitting (y = (1-α)y1 + αy2), so that a simple MSE or negative-log-likelihood loss on (y1, y2) is an unbiased estimator of the supervised loss; as α→0 it reduces to a SURE-type loss without computing divergences.
Key results
- On log-Rayleigh noise, GR2R with third-moment correction reaches 29.47 dB PSNR versus 25.32 dB for R2R and 29.93 dB for supervised learning.
- On Poisson denoising at gain 0.01, GR2R-MSE reaches 33.92 dB vs 33.96 dB for supervised MSE and 33.37 dB for Neigh2Neigh.
- On Gaussian noise at sigma=0.5 on fastMRI, GR2R attains 25.81 dB PSNR vs 25.93 dB supervised and 25.61 dB for Neigh2Neigh.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add GR2R recorruption with third-order moment matching instead of standard R2R second-moment matching (ablation) | R2R on DIV2K log-Rayleigh denoising · Additive log-Rayleigh noise | PSNR: 25.32 ± 0.79 -> 29.93 ± 1.50 | Helped |
| Use GR2R-NLL rather than GR2R-MSE (ablation) | GR2R on DIV2K Poisson denoising · Poisson noise, γ=0.5 | PSNR: 24.69 -> 25.07 | Helped |
| Use GR2R-MSE rather than GR2R-NLL (ablation) | GR2R on DIV2K Poisson denoising · Poisson noise, γ=0.01 | PSNR: 33.90 -> 33.92 | No clear effect |
| Use GR2R-MSE rather than GR2R-NLL (ablation) | GR2R on SAR Gamma denoising · Gamma noise, ℓ=30 | PSNR: 30.43 -> 31.58 | Helped |
| Use GR2R-MSE rather than GR2R-NLL (ablation) | GR2R on SAR Gamma denoising · Gamma noise, ℓ=1 | PSNR: 22.19 -> 22.38 | No clear effect |
| Train with GR2R rather than Noise2Score | Image denoising on fastMRI · Gaussian noise, σ=0.05 | PSNR: 34.42 -> 35.38 | Helped |
| Train with GR2R rather than SURE | Image denoising on fastMRI · Gaussian noise, σ=0.05 | PSNR: 35.31 -> 35.38 | No clear effect |
| Train with GR2R rather than supervised MSE | Image denoising on fastMRI · Gaussian noise, σ=0.05 | PSNR: 35.41 -> 35.38 | No clear effect |
| Train with GR2R-MSE rather than Neigh2Neigh | SAR Gamma denoising · Gamma noise, ℓ=30 | PSNR: 30.34 -> 31.58 | Helped |
| Train with GR2R-NLL rather than Neigh2Neigh | DIV2K Poisson denoising · Poisson noise, γ=0.5 | PSNR: 24.90 -> 25.07 | Helped |
Surprising findings
- On Gamma noise with 1 look, GR2R-NLL matches Neigh2Neigh PSNR (22.19 dB) and GR2R-MSE is slightly higher (22.38 dB), with performance gap to supervised closing at low SNR.
- The MSE variant of GR2R performs worse than the NLL variant in the low-count Poisson regime (e.g., 0.5 gain: 24.69 vs 25.07 dB).
Limitations
- Gaussian-noise results on fastMRI are only a slight gain over other self-supervised methods, and performance is below supervised training at moderate noise.
- When the forward operator is rank-deficient, the GR2R minimizer is not the MMSE estimator and additional invariance or multi-operator assumptions (e.g., Equivariant Imaging) are needed.
- Gamma-noise experiments are limited to SAR despeckling with a single dataset, and the splitting for the high-order moment case requires a maximum-entropy sampling procedure.
Experimental setup
Datasets: DIV2K SAR Image Despeckling dataset fastMRI
Benchmarks: DIV2K SAR Image Despeckling dataset fastMRI
Metrics: PSNR SSIM
Baselines: R2R SURE PURE Neigh2Neigh Noise2Score Equivariant Imaging Supervised MSE
Builds on: Recorrupted-to-Recorrupted (R2R) Stein's unbiased risk estimator (SURE) Noise2Noise Equivariant Imaging GSURE
Closest papers by meaning
- Recorrupted-to-Recorrupted: Unsupervised Deep Learning for Image Denoising (CVPR 2021 · similarity 0.89)
- UNSURE: self-supervised learning with Unknown Noise level and Stein's Unbiased Risk Estimate (ICLR 2025 · similarity 0.85)
- Stochastic Deep Restoration Priors for Imaging Inverse Problems (ICML 2025 · similarity 0.84)
- APR-RD: Complemental Two Steps for Self-Supervised Real Image Denoising (AAAI 2025 · similarity 0.84)
- Ditch the Denoiser: Emergence of Noise Robustness in Self-Supervised Learning from Data Curriculum (NeurIPS 2025 · similarity 0.83)
- Positive2Negative: Breaking the Information-Lossy Barrier in Self-Supervised Single Image Denoising (CVPR 2025 · similarity 0.83)
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