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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 refid="ref1"/, refid="ref2"/. 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. [ABSTRACT FROM AUTHOR]

Multiplicative noise removal based on total variation (TV) regularization has been widely researched in image science. In this paper, inspired by the spatially adapted methods for denoising Gaussian noise, we develop a variational model, which combines the TV regularizer with local constraints. It is also related to a TV model with spatially adapted regularization parameters. The automated selection of the regularization parameters is based on the local statistical characteristics of some random variable. The corresponding subproblem can be efficiently solved by the augmented Lagrangian method. Numerical examples demonstrate that the proposed algorithm is able to preserve small image details, whereas the noise in the homogeneous regions is sufficiently removed. As a consequence, our method yields better denoised results than those of the current state-of-the-art methods with respect to the signal-to-noise-ratio values. [ABSTRACT FROM AUTHOR]