Self-supervised learning for image denoising problems in the presence of denaturation for noisy data is a crucial approach in machine learning. However, theoretical understanding of the performance of the approach that uses denatured data is lacking. To provide better understanding of the approach, in this paper, we analyze a self-supervised denoising algorithm that uses denatured data in depth through theoretical analysis and numerical experiments. Through the theoretical analysis, we discuss that the algorithm finds desired solutions to the optimization problem with the population risk, while the guarantee for the empirical risk depends on the hardness of the denoising task in terms of denaturation levels. We also conduct several experiments to investigate the performance of an extended algorithm in practice. The results indicate that the algorithm training with denatured images works, and the empirical performance aligns with the theoretical results. These results suggest several insights for further improvement of self-supervised image denoising that uses denatured data in future directions.

翻译：针对含噪声数据中存在变性情况的自监督图像去噪问题，是机器学习中的关键研究方法。然而，目前缺乏对使用变性数据的该方法性能的理论理解。为深化对该方法的认识，本文通过理论分析与数值实验，深入剖析了利用变性数据的自监督去噪算法。理论分析表明，该算法在总体风险下能够找到优化问题的期望解，而经验风险的保证程度取决于去噪任务中变性水平的难度。我们进一步开展多项实验，探究扩展算法在实际场景中的性能表现。实验结果表明，采用变性图像训练的算法有效，且实际性能与理论结果吻合。这些发现为未来利用变性数据的自监督图像去噪方法的优化提供了重要启示。