Below the Surface of the Non-Local Bayesian Image Denoising Method

With Mila Nikolova (speaker) and co-author Pablo Arias from ENS Cachan

Below the Surface of the Non-Local Bayesian Image Denoising Method

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 rami*fications like e.g., possible improvements, processing of various data sets and video. This article 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.

This is joint work with Pablo Arias.

[1] Lebrun, M., Buades, A., Morel, J.M.: A nonlocal Bayesian image denoising algorithm. SIAM J . Imaging Sci.6(3), 1665-1688 (2013)

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