Nonlocal image deblurring: Variational formulation with nonlocal collaborative L0-norm prior

Spatially adaptive nonlocal patch-wise estimation is one of the most promising recent directions in image processing. Within this framework a set of the state-of-the-art Block Matching 3-D (BM3D) algorithms has been developed for different imaging problems. Recently, a special prior hoas been proposed allowing to reformulate the multi-state hard-thresholding BM3D denoising as global minimization of an energy criterion. The out-standing performance of BM3D works as a strong argument in favor of this prior giving an efficient multilayer redundant image model. The variational formulation is used in order to design a novel recursive denoising algorithm. In this paper the nonlocal collaborative l₀-norm prior is a tool to design deblurring algorithms, where the global penalty function works as an adaptive regularizator. The main contribution concerns the development and testing of algebraic and frequency domain recursive algorithms minimizing the global criterion. Simulation demonstrate a very good performance of the novel algorithms.