title: BM3D frames and variational image deblurring.
abstract: A family of the block matching 3-D (BM3D) algorithms for various imaging problems has been recently proposed within the framework of nonlocal patchwise image modeling ,  . In this paper, we construct analysis and synthesis frames, formalizing BM3D image modeling, and use these frames to develop novel iterative deblurring algorithms. We consider two different formulations of the deblurring problem, i.e., one given by the minimization of the single-objective function and another based on the generalized Nash equilibrium (GNE) balance of two objective functions. The latter results in the algorithm where deblurring and denoising operations are decoupled. The convergence of the developed algorithms is proved. Simulation experiments show that the decoupled algorithm derived from the GNE formulation demonstrates the best numerical and visual results and shows superiority with respect to the state of the art in the field, confirming a valuable potential of BM3D-frames as an advanced image modeling tool.
authors: Department of Signal Processing, Tampere University of Technology, Tampere, Finland. aram.danielyan@tut.fi
authors: Aram
authors: A
authors: Danielyan
authors: Vladimir
authors: V
authors: Katkovnik
authors: Karen
authors: K
authors: Egiazarian
mesh_terms: D000465:Algorithms; D016477:Artifacts; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D015233:Models, Statistical; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted