5. Gaussian Priors for Image Denoising

This chapter is dedicated to the study of Gaussian priors for patch-based image denoising. In the last 12 years, patch priors have been widely used for image restoration. In a Bayesian framework, such priors on patches can be used for instance to estimate a clean patch from its noisy version, via classical estimators such as the conditional expectation or the maximum a posteriori. As we will recall, in the case of Gaussian white noise, simply assuming Gaussian (or Mixture of Gaussians) priors on patches leads to very simple closed-form expressions for some of these estimators. Nevertheless, the convenience of such models should not prevail over their relevance. For this reason, we also discuss how these models represent patches and what kind of information they encode. The end of the chapter focuses on the different ways in which these models can be learned on real data. This stage is particularly challenging because of the curse of dimensionality. Through these different questions, we compare and connect several denoising methods using this framework.