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：在噪声数据存在变性的情况下，自监督学习对于图像去噪问题而言是机器学习中的一种关键方法。然而，目前对于使用变性数据的方法的性能尚缺乏理论上的理解。为了增进对该方法的理解，本文通过理论分析和数值实验，深入分析了一种使用变性数据的自监督去噪算法。通过理论分析，我们论证了该算法能够找到基于总体风险的优化问题的期望解，而关于经验风险的保证则取决于去噪任务在变性程度方面的难度。我们还进行了多项实验，以探究一种扩展算法在实际中的性能。结果表明，使用变性图像进行算法训练是有效的，且其实验性能与理论结果相符。这些结果为未来进一步改进使用变性数据的自监督图像去噪方法提供了若干启示。