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：在机器学习的图像去噪问题中，针对含有变性噪声的数据进行自监督学习是一种重要方法。然而，目前对利用变性数据的方法在理论上的性能理解尚不充分。为加深对此方法的认识，本文通过理论分析与数值实验，深入探究了一种使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寻得优化问题的理想解，而经验风险的保证则取决于去噪任务在变性程度上的难度。此外，我们开展了多项实验以评估扩展算法在实际中的表现。结果表明，基于变性图像训练的算法有效，且实验性能与理论结果相吻合。这些发现为未来利用变性数据的自监督图像去噪方法的进一步改进提供了若干启示。