Tutorial 1: Nonlocal Image Processing Techniques: Overview and Advanced Developments

Presented by

Vladimir Katkovnik, Tampere University of Technology

Abstract

Nonlocal imaging techniques look for patches (blocks, fragments) which are similar to each other and process these patches jointly. A proper use of the similarity is a nontrivial problem and being appropriate results in a good and even extraordinary good performance. This sort of techniques appeared independently in number of various developments with an intensive flow of recent publications.

One of the goals of this tutorial is a pragmatic and clear review of the nonlocal techniques which can serve as a guideline in this intensively developing area. We present various methods and algorithms as an evolution of the nonlocal image modeling starting from the local kernel estimation, going to the nonlocal means (NL-means) and further to transform-domain filtering based on block-matching. The models are classified according to two main features: local/nonlocal and pointwise/multipoint. These alternatives, though obvious simplifications, allow a fruitful and transparent presentation of ideas and algorithms of the modern advanced techniques. In the multipoint case the data are typically processed by overlapping subsets (windows, blocks or generic neighborhoods) and multiple estimates obtained for each individual point. The Â…nal estimate is calculated by aggregating (fusing) the multiple estimates. The Block Matching and 3-D Filtering (BM3D) algorithm, which is currently one of the best performing denoising algorithms, is an example of this sort of non-local spatially adaptive techniques. As a recent development we present a novel image modeling based on the collaborative l_0-norm prior. This prior allows to develop a variational formulation for some efficient nonlocal techniques. Minimization of the energy criteria with this prior is used to design new recursive procedures demonstrating performance overcoming some of state-of-the-art algorithms.

We consider modeling and algorithms for the following imaging problems: denoising (Gaussian and non-Gaussian), deblurring (deconvolution), compressive sensing, color image processing including demosaicking, etc.

The tutorial is accompanied by numerous examples where the nonlocal methods are applied. Matlab codes implementing the nonlocal image processing techniques, demos and publications can be found on website: http://www.cs.tut.fi/~foi/.