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.

Color image reconstruction from noisy color Þlter array (CFA) data is considered. A modiÞcation of the Block Matching 3D (BM3D) [2] Þlter for CFA data denoising utilizing cross-color correlations is proposed. Denoised images are then demosaicked by algorithms developed for noise-free data leading to state-of-the-art performance for both Gaussian and Poissonian noise models.

We consider the estimation of the variance of an additive white Gaussian noise corrupting an image.In the proposed approach, we exploit the nonlocal selfsimilarity of images to achieve an improved separation of noise and signal. In particular, we utilize the same adaptive 3-D transform decomposition used in the BM3D (blockmatching and 3-D Þltering) denoising algorithm, where mutually similar blocks are stacked together and jointly processed. An adaptive-size portion of the high-frequency ends of the 3-D transform spectra is retained and used as input sample for a robust median estimator of the absolute deviation.Experimental analysis demonstrate a state-of-the-art accuracy of the proposed approach.

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