# Denoising: from classical methods to deep CNNs

arXiv: https://arxiv.org/abs/2404.16617 · HTML: https://mlsanity.com/paper/2404.16617/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 53 references that are in the map.
- First posted on arXiv 25 Apr 2024.

## Builds on (most cited first, 10 of 10)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Efficient Processing of Deep Neural Networks: A Tutorial and Survey](https://mlsanity.com/paper/1703.09039/) (2017)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Separation and Concentration in Deep Networks](https://mlsanity.com/paper/2012.10424/) (2020)
- [Deep Network Classification by Scattering and Homotopy Dictionary Learning](https://mlsanity.com/paper/1910.03561/) (2019)
- [Scattering Spectra Models for Physics](https://mlsanity.com/paper/2306.17210/) (2023)
- [A Comparison of Image Denoising Methods](https://mlsanity.com/paper/2304.08990/) (2023)

## Abstract (arXiv)

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.