On the Posterior Distribution in Denoising: Application to Uncertainty Quantification
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914684418916352 |
|---|---|
| author | Manor, Hila Michaeli, Tomer |
| author_facet | Manor, Hila Michaeli, Tomer |
| contents | 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 (\ie 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. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_13598 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Posterior Distribution in Denoising: Application to Uncertainty Quantification Manor, Hila Michaeli, Tomer Computer Vision and Pattern Recognition Machine Learning 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 (\ie 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. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ . |
| title | On the Posterior Distribution in Denoising: Application to Uncertainty Quantification |
| topic | Computer Vision and Pattern Recognition Machine Learning |
| url | https://arxiv.org/abs/2309.13598 |