This paper aims to explore the evolution of image denoising in a
pedagological way. We briefly review classical methods such as Fourier analysis
and wavelet bases, highlighting the challenges they faced until the emergence
of neural networks, notably the U-Net, in the 2010s. The remarkable performance
of these networks has been demonstrated in studies such as Kadkhodaie et al.
(2024). They exhibit adaptability to various image types, including those with
fixed regularity, facial images, and bedroom scenes, achieving optimal results
and biased towards geometry-adaptive harmonic basis. The introduction of score
diffusion has played a crucial role in image generation. In this context,
denoising becomes essential as it facilitates the estimation of probability
density scores. We discuss the prerequisites for genuine learning of
probability densities, offering insights that extend from mathematical research
to the implications of universal structures.

该论文探讨图像去噪的演变过程，从傅里叶分析和小波基础方法到神经网络，尤其是 U-Net 的出现。神经网络在 2010 年代的研究中展现出卓越的性能，适用于各种图像类型，包括具有固定规律性、人脸图像和卧室场景，以及对几何适应性调和基础有偏好的结果。引入分数扩散在图像生成中起着关键作用，图像去噪在这一背景下变得至关重要，因为它有助于概率密度的估计。我们讨论了真实学习概率密度的先决条件，并提供了从数学研究到通用结构的深入洞察。