Nonlocal Collaborative l0-Norm Prior for Image Denoising

Spatially adaptive nonparametric regression estimation is one of the most promising recent directions in image processing. The Transforms and Spectral Techniques Research Group at the Department of Signal Processing, Tampere University of Technology, has been active in this novel …eld starting from about 2002. The results achieved with application to di¤erent image and video processing problems are very positive and completely support optimism following from general speculations concerning nonparametric modeling (e.g. [1]-[9]). Within this framework the Block Matching and 3-D Filtering (BM3D) algorithm has been developed which is currently one of the best performing denoising algorithms. In this paper a special prior is proposed allowing to reformulate mainly semi-heuristic nonlocal nonparametric techniques as global minimization of an energy criterion. It is shown that the basic hard-thresholding part of the BM3D algorithm can be derived as a minimizer of the proposed prior. The outstanding performance of BM3D is a strong argument in favor of this prior as an e¢ cient multilayer redundant image model.