Explicit Diffusion of Gaussian Mixture Model Based Image Priors

TL;DR

This paper introduces a Gaussian mixture model-based image prior that explicitly diffuses through a smoothing process, enabling effective denoising, noise estimation, and interpretability with a small parameter set.

Contribution

It presents a novel analytic Gaussian mixture diffusion model for image priors that is trainable over the entire diffusion process and applicable to blind denoising.

Findings

Competitive image denoising results

Effective noise estimation for heteroscedastic noise

Model is tractable and interpretable

Abstract

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 $(\partial_t - \Delta_1)f_Y(\,\cdot\,, t) = 0$, $f_Y(\,\cdot\,, 0) = f_X$. 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.