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arXiv 2404.16617cs.CVmath.HO

去噪:从经典方法到深度CNN

Denoising: from classical methods to deep CNNs

Jean-Eric Campagne

AI总结:

本文以教学方式回顾图像去噪从经典方法到深度CNN的演变,探讨U-Net和score diffusion在去噪与图像生成中的关键作用及概率密度学习的前提。

摘要:

本文旨在以教学方式探讨图像去噪的演变。我们简要回顾了Fourier分析和wavelet bases等经典方法,强调了它们在2010年代神经网络(尤其是U-Net)出现之前所面临的挑战。这些网络的卓越性能已在Kadkhodaie et al. (2024)等研究中得到证明。它们对多种图像类型表现出适应性,包括具有固定规律性的图像、人脸图像和卧室场景,取得了最优结果并偏向于几何自适应谐波基。score diffusion的引入在图像生成中发挥了关键作用。在此背景下,去噪变得至关重要,因为它有助于估计概率密度分数。我们讨论了真正学习概率密度的前提条件,提供了从数学研究到普遍结构意义的见解。

英文摘要:

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.

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