# UNSURE: self-supervised learning with Unknown Noise level and Stein's Unbiased Risk Estimate

arXiv: https://arxiv.org/abs/2409.01985 · HTML: https://mlsanity.com/paper/2409.01985/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2024.

## Built on by (most cited first, 16 of 16)

- [MRI Super-Resolution with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2511.16854/) (2025)
- [Noisier2Inverse: Self-Supervised Learning for Image Reconstruction with Correlated Noise](https://mlsanity.com/paper/2503.19468/) (2025)
- [Self-Supervised Learning from Noisy and Incomplete Data](https://mlsanity.com/paper/2601.03244/) (2026)
- [Robust multi-coil MRI reconstruction via self-supervised denoising](https://mlsanity.com/paper/2411.12919/) (2024)
- [Benchmarking Self-Supervised Learning Methods for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2502.14009/) (2025)
- [Normalization-equivariant Diffusion Models: Learning Posterior Samplers From Noisy And Partial Measurements](https://mlsanity.com/paper/2510.11964/) (2025)
- [Whiteness-based bilevel estimation of weighted TV parameter maps for image denoising](https://mlsanity.com/paper/2503.07814/) (2025)
- [Reconstruct Anything Model: a lightweight general model for computational imaging](https://mlsanity.com/paper/2503.08915/) (2025)
- [Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problems](https://mlsanity.com/paper/2503.16222/) (2025)
- [Restarted contractive operators to learn at equilibrium](https://mlsanity.com/paper/2506.13239/) (2025)
- [Equivariant Splitting: Self-supervised learning from incomplete data](https://mlsanity.com/paper/2510.00929/) (2025)
- [Learning to Recorrupt: Noise Distribution Agnostic Self-Supervised Image Denoising](https://mlsanity.com/paper/2603.25869/) (2026)
- [HyDRA: Hybrid Denoising Regularization for Measurement-Only DEQ Training](https://mlsanity.com/paper/2601.01228/) (2026)
- [Equivariant Learning for Unsupervised Image Dehazing](https://mlsanity.com/paper/2601.13986/) (2026)
- [Self-Supervised Uncertainty Estimation For Super-Resolution of Satellite Images](https://mlsanity.com/paper/2603.14074/) (2026)
- [Frozen CLIP Priors for Robust Self-Supervised Poisson Inverse Problems](https://mlsanity.com/paper/2608.20524/) (2026)

## Abstract (arXiv)

Recently, many self-supervised learning methods for image reconstruction have been proposed that can learn from noisy data alone, bypassing the need for ground-truth references. Most existing methods cluster around two classes: i) Stein's Unbiased Risk Estimate (SURE) and similar approaches that assume full knowledge of the noise distribution, and ii) Noise2Self and similar cross-validation methods that require very mild knowledge about the noise distribution. The first class of methods tends to be impractical, as the noise level is often unknown in real-world applications, and the second class is often suboptimal compared to supervised learning. In this paper, we provide a theoretical framework that characterizes this expressivity-robustness trade-off and propose a new approach based on SURE, but unlike the standard SURE, does not require knowledge about the noise level. Throughout a series of experiments, we show that the proposed estimator outperforms other existing self-supervised methods on various imaging inverse problems.