On the Posterior Distribution in Denoising:
Application to Uncertainty Quantification

ICLR 2024

Hila Manor
Tomer Michaeli

Technion - Israel Institute of Technology

ArXiv
Code
OpenReview

Abstract

Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (i.e., the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser.

Uncertainty Visualization

We propose an efficient way to compute the principal components of the posterior distribution.

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Estimation of Marginal Distribution along Directions

We also propose an efficient way to estimate a more fine-grained characterization of the posterior by using higher-order moments along the computed principal directions.

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More Samples


Paper

On the Posterior Distribution in Denoising: Application to Uncertainty Quantification
Hila Manor, Tomer Michaeli.


Arxiv

Code

Bibtex

@inproceedings{
    manor2024posterior,
    title={On the Posterior Distribution in Denoising: Application to Uncertainty Quantification},
    author={Hila Manor and Tomer Michaeli},
    booktitle={The Twelfth International Conference on Learning Representations},
    year={2024},
    url={https://openreview.net/forum?id=adSGeugiuj}
}

More results and further discussion about our method can be found in the supplementary material (included in the paper).


Recent Related Work

Recently the field of uncertainty quantification and its applications have witnessed a number of interesting works in the area of semantic uncertainty. If this work interested you, you might also want to take a look at the following works that dealt with semantic uncertainty:

You might also be interested in these related and follow-up works from our lab:


Acknowledgements

This webpage was originally made by Matan Kleiner with the help of Hila Manor for SinDDM and can be used as a template.
It is inspired by the template that was originally made by Phillip Isola and Richard Zhang for a colorful ECCV project; the code for the original template can be found here.
A lot of features are taken from bootstrap. All icons are taken from font awesome.