TY - GEN
T1 - Explicit Diffusion of Gaussian Mixture Model Based Image Priors
AU - Zach, Martin
AU - Pock, Thomas
AU - Kobler, Erich
AU - Chambolle, Antonin
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2023
Y1 - 2023
N2 - In this work we tackle the problem of estimating the density fX of a random variable X by successive smoothing, such that the smoothed random variable Y fulfills (∂t-Δ1)fY(·,t)=0, fY(·,0)=fX. With a focus on image processing, we propose a product/fields-of-experts model with Gaussian mixture experts that admits an analytic expression for fY(·,t) under an orthogonality constraint on the filters. This construction naturally allows the model to be trained simultaneously over the entire diffusion horizon using empirical Bayes. We show preliminary results on image denoising where our model leads to competitive results while being tractable, interpretable, and having only a small number of learnable parameters. As a byproduct, our model can be used for reliable noise estimation, allowing blind denoising of images corrupted by heteroscedastic noise.
AB - In this work we tackle the problem of estimating the density fX of a random variable X by successive smoothing, such that the smoothed random variable Y fulfills (∂t-Δ1)fY(·,t)=0, fY(·,0)=fX. With a focus on image processing, we propose a product/fields-of-experts model with Gaussian mixture experts that admits an analytic expression for fY(·,t) under an orthogonality constraint on the filters. This construction naturally allows the model to be trained simultaneously over the entire diffusion horizon using empirical Bayes. We show preliminary results on image denoising where our model leads to competitive results while being tractable, interpretable, and having only a small number of learnable parameters. As a byproduct, our model can be used for reliable noise estimation, allowing blind denoising of images corrupted by heteroscedastic noise.
KW - Blind Denoising
KW - Diffusion Models
KW - Empirical Bayes
KW - Gaussian Mixture
UR - http://www.scopus.com/inward/record.url?scp=85161183670&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-31975-4_1
DO - 10.1007/978-3-031-31975-4_1
M3 - Conference paper
AN - SCOPUS:85161183670
SN - 9783031319747
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 3
EP - 15
BT - Scale Space and Variational Methods in Computer Vision - 9th International Conference, SSVM 2023, Proceedings
A2 - Calatroni, Luca
A2 - Donatelli, Marco
A2 - Morigi, Serena
A2 - Prato, Marco
A2 - Santacesaria, Matteo
PB - Springer Science and Business Media Deutschland GmbH
T2 - 9th International Conference on Scale Space and Variational Methods in Computer Vision
Y2 - 21 May 2023 through 25 May 2023
ER -