Explicit Diffusion of Gaussian Mixture Model Based Image Priors
This work addresses image denoising with a tractable and interpretable model, but it is incremental as it builds on existing diffusion and mixture model approaches.
The authors tackled the problem of estimating probability densities via diffusion for image processing, proposing a Gaussian mixture model that yields competitive denoising results with tractability and interpretability, achieving reliable noise estimation for blind denoising of heteroscedastic noise.
In this work we tackle the problem of estimating the density $f_X$ of a random variable $X$ by successive smoothing, such that the smoothed random variable $Y$ fulfills $(\partial_t - Δ_1)f_Y(\,\cdot\,, t) = 0$, $f_Y(\,\cdot\,, 0) = f_X$. With a focus on image processing, we propose a product/fields of experts model with Gaussian mixture experts that admits an analytic expression for $f_Y (\,\cdot\,, t)$ 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.