From Local Kernel to Nonlocal Multiple-Model Image Denoising

Authors:
Vladimir Katkovnik;Alessandro Foi;Karen Egiazarian;Jaakko Astola
Affiliations:
Department of Signal Processing, Tampere University of Technology, Tampere, Finland;Department of Signal Processing, Tampere University of Technology, Tampere, Finland;Department of Signal Processing, Tampere University of Technology, Tampere, Finland;Department of Signal Processing, Tampere University of Technology, Tampere, Finland
Venue:
International Journal of Computer Vision
Year:
2010

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Abstract

We review the evolution of the nonparametric regression modeling in imaging from the local Nadaraya-Watson kernel estimate to the nonlocal means and further to transform-domain filtering based on nonlocal block-matching. The considered methods are classified mainly according to two main features: local/nonlocal and pointwise/multipoint. Here nonlocal is an alternative to local, and multipoint is an alternative to pointwise. These alternatives, though obvious simplifications, allow to impose a fruitful and transparent classification of the basic ideas in the advanced techniques. Within this framework, we introduce a novel single- and multiple-model transform domain nonlocal approach. The Block Matching and 3-D Filtering (BM3D) algorithm, which is currently one of the best performing denoising algorithms, is treated as a special case of the latter approach.