Natural Image Statistics, Visual Representation, and Denoising

Imran Thobani, Alisa Leshchenko, Eero P Simoncelli
Proceedings of the Analytical Connectionism Schools 2023--2024, PMLR 320:102-112, 2026.

Abstract

This article, gathered and elaborated from a lecture by Eero Simoncelli at the 2024 Analytical Connectionism Summer School, reviews several approaches for modeling the probabilistic distribution of natural images and their interaction with the problem of image denoising. The lecture starts with the Gaussian spectral model of the 1950s as a conceptual foundation and quantitative baseline, followed by sparse coding models which took hold in the 1990s. These statistical models of natural images can be used as prior probability distributions for solving inverse problems such as denoising, using a Bayesian framework. Finally, the lecture describes recent work in machine learning in which the process of constructing a denoiser is reversed: a neural network is trained to solve the denoising problem without first specifying a prior distribution, and this trained network is subsequently used as an implicit model of the distribution of natural images. Images can be drawn from this implicit model through a reverse diffusion process, and the model can also be used to solve inference problems. This allows researchers to investigate the extent to which these DNNs are generalizing beyond their training data (as necessary for accurately modeling the distribution of natural images) as opposed to memorizing the images they were trained on.

Cite this Paper

BibTeX
@InProceedings{pmlr-v320-thobani26a, title = {Natural Image Statistics, Visual Representation, and Denoising}, author = {Thobani, Imran and Leshchenko, Alisa and Simoncelli, Eero P}, booktitle = {Proceedings of the Analytical Connectionism Schools 2023--2024}, pages = {102--112}, year = {2026}, editor = {Sarao Mannelli, Stefano and Mignacco, Francesca and Chou, Chi-Ning and Chung, SueYeon and Saxe, Andrew}, volume = {320}, series = {Proceedings of Machine Learning Research}, month = {01 Jan--31 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v320/main/assets/thobani26a/thobani26a.pdf}, url = {https://proceedings.mlr.press/v320/thobani26a.html}, abstract = {This article, gathered and elaborated from a lecture by Eero Simoncelli at the 2024 Analytical Connectionism Summer School, reviews several approaches for modeling the probabilistic distribution of natural images and their interaction with the problem of image denoising. The lecture starts with the Gaussian spectral model of the 1950s as a conceptual foundation and quantitative baseline, followed by sparse coding models which took hold in the 1990s. These statistical models of natural images can be used as prior probability distributions for solving inverse problems such as denoising, using a Bayesian framework. Finally, the lecture describes recent work in machine learning in which the process of constructing a denoiser is reversed: a neural network is trained to solve the denoising problem without first specifying a prior distribution, and this trained network is subsequently used as an implicit model of the distribution of natural images. Images can be drawn from this implicit model through a reverse diffusion process, and the model can also be used to solve inference problems. This allows researchers to investigate the extent to which these DNNs are generalizing beyond their training data (as necessary for accurately modeling the distribution of natural images) as opposed to memorizing the images they were trained on.} }
Endnote
%0 Conference Paper %T Natural Image Statistics, Visual Representation, and Denoising %A Imran Thobani %A Alisa Leshchenko %A Eero P Simoncelli %B Proceedings of the Analytical Connectionism Schools 2023--2024 %C Proceedings of Machine Learning Research %D 2026 %E Stefano Sarao Mannelli %E Francesca Mignacco %E Chi-Ning Chou %E SueYeon Chung %E Andrew Saxe %F pmlr-v320-thobani26a %I PMLR %P 102--112 %U https://proceedings.mlr.press/v320/thobani26a.html %V 320 %X This article, gathered and elaborated from a lecture by Eero Simoncelli at the 2024 Analytical Connectionism Summer School, reviews several approaches for modeling the probabilistic distribution of natural images and their interaction with the problem of image denoising. The lecture starts with the Gaussian spectral model of the 1950s as a conceptual foundation and quantitative baseline, followed by sparse coding models which took hold in the 1990s. These statistical models of natural images can be used as prior probability distributions for solving inverse problems such as denoising, using a Bayesian framework. Finally, the lecture describes recent work in machine learning in which the process of constructing a denoiser is reversed: a neural network is trained to solve the denoising problem without first specifying a prior distribution, and this trained network is subsequently used as an implicit model of the distribution of natural images. Images can be drawn from this implicit model through a reverse diffusion process, and the model can also be used to solve inference problems. This allows researchers to investigate the extent to which these DNNs are generalizing beyond their training data (as necessary for accurately modeling the distribution of natural images) as opposed to memorizing the images they were trained on.
APA
Thobani, I., Leshchenko, A. & Simoncelli, E.P.. (2026). Natural Image Statistics, Visual Representation, and Denoising. Proceedings of the Analytical Connectionism Schools 2023--2024, in Proceedings of Machine Learning Research 320:102-112 Available from https://proceedings.mlr.press/v320/thobani26a.html.

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