An Empirical Bayesian interpretation and generalization of NL-means

A number of recent algorithms in signal and image processing are based on the empirical distribution of localized patches. Here, we develop a nonparametric empirical Bayesian estimator for recovering an image corrupted by additive Gaussian noise, based on fitting the density over image patches with a local exponential model. The resulting solution is in the form of an adaptively weighted average of the observed patch with the mean of a set of similar patches, and thus both justifies and generalizes the recently proposed nonlocalmeans (NL-means) method for image denoising. Unlike NL-means, our estimator includes a dependency on the size of the patch similarity neighborhood, and we show that this neighborhood size can be chosen in such a way that the estimator converges to the optimal Bayes least squares estimator as the amount of data grows. We demonstrate the increase in performance of our method compared to NL-means on a set of simulated examples.