Authors: Martin Raphan  and  Eero P. Simoncelli


Title: An Empirical Bayesian interpretation and generalization of NL-means

 Abstract: 
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  nonlocal-means (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.