From Local Kernel to Nonlocal Multiple-Model Image Denoising

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 Þltering based on nonlocal block-matching. The considered methods are classiÞed 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 simpliÞcations, allow to impose a fruitful and transparent classiÞcation of the basic ideas in the advanced techniques. Within this framework, we introduce a novel single- and multiplemodel 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.

• Type: Journal
• Year: 2010
• Where: IJCV
• Authors: Vladimir Katkovnik, Alessandro Foi, Karen Egiazarian, Jaakko Astola
• Keywords: IJCV 2010, Nonlocal, Nonlocal Means, Nonparametric Regression Modeling