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

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• Mila Nikolova (speaker) and co-author Pablo Arias from ENS Cachan
• Monday 17 July 2017, 13:00-14:00
• MR 14, Centre for Mathematical Sciences.

If you have a question about this talk, please contact Carola-Bibiane Schoenlieb.

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.

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

This talk is part of the Cambridge Image Analysis Seminars series.

This talk is included in these lists:

• Cambridge Image Analysis Seminars
• MR 14, Centre for Mathematical Sciences

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