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.

本文通过理论分析和数值实验深入分析了使用变性数据的自监督降噪算法，讨论了该算法在优化问题的种群风险上找到期望解的同时，经验风险的保证则取决于变性水平对降噪任务的难度。实验结果表明，使用变性图像进行训练的算法起作用，并且经验性能与理论结果相一致，为今后使用变性数据进行自监督图像降噪的进一步改进提供了一些见解。