Abstract
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.
Abstract (translated)
本文旨在以教育性的方式探讨图像去噪的演变。我们简要回顾了经典方法，如傅里叶分析和小波基，并着重指出它们在21世纪之前所面临到的挑战，特别是U-Net。这些网络的非凡性能已在像Kadkhodaie等人（2024）这样的研究中得到证实。它们表现出对各种图像类型的适应性，包括具有固定规范的图像、面部图像和卧室场景，实现最佳结果并倾向于几何自适应小波基。引入分数扩散在图像生成中发挥了关键作用。在这种背景下，去噪变得至关重要，因为它有助于概率密度分数的估计。我们讨论了真正学习概率密度的先决条件，将数学研究的见解扩展到普遍结构的意义上。
URL
https://arxiv.org/abs/2404.16617
