Abstract

joint work with Pablo Arias CMLA , ENS Cachan, CNRS , University Paris-Saclay The non-local Bayesian (NLB) patch-based approach of Lebrun, Buades, and Morel [1] is considered as a state-of-the-art method for the restoration of (color) images corrupted by white Gaussian noise. It gave rise to numerous ramiifications like e.g., possible improvements, processing of various data sets and video. This work is the first attempt to analyse the method in depth in order to understand the main phenomena underlying its effectiveness. Our analysis, corroborated by numerical tests, shows several unexpected facts. In a variational setting, the first-step Bayesian approach to learn the prior for patches is equivalent to a pseudo-Tikhonov regularisation where the regularisation parameters can be positive or negative. Practically very good results in this step are mainly due to the aggregation stage – whose importance needs to be re-evaluated. Reference [1] Lebrun, M., Buades, A., Morel, J.M.: A nonlocal Bayesian image denoising algorithm. SIAM J . Imaging Sci.6(3), 1665-1688 (2013)