Abstract
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 the diffusion partial differential equation (∂t-Δ1)fY(·,t)=0 with initial condition fY(·,0)=fX. We propose a product-of-experts-type model utilizing Gaussian mixture experts and study configurations that admit an analytic expression for fY(·,t). In particular, with a focus on image processing, we derive conditions for models acting on filter, wavelet, and shearlet responses. Our construction naturally allows the model to be trained simultaneously over the entire diffusion horizon using empirical Bayes. We show numerical results for image denoising where our models are competitive while being tractable, interpretable, and having only a small number of learnable parameters. As a by-product, our models can be used for reliable noise level estimation, allowing blind denoising of images corrupted by heteroscedastic noise.
Original language | English |
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Journal | Journal of Mathematical Imaging and Vision |
DOIs | |
Publication status | Accepted/In press - 2024 |
Keywords
- Blind denoising
- Diffusion models
- Empirical bayes
- Gaussian mixture
ASJC Scopus subject areas
- Statistics and Probability
- Modelling and Simulation
- Condensed Matter Physics
- Computer Vision and Pattern Recognition
- Geometry and Topology
- Applied Mathematics