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

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 expressivityrobustness 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. 1 1. We present a theoretical framework for understanding the robustness-expressivity trade-off of different self-supervised learning methods.

2. We propose a new self-supervised objective that extends the SURE loss for the case where the noise level is unknown, and provide generalizations to spatially correlated Gaussian noise