Adaptive shearlet-regularized image deblurring via alternating direction method

Unlike the traditional wavelets, which lack the ability to detect directionality, shearlets provide a multidirectional as well as multiscale decomposition for multidimension signals. In this paper, we propose a new adaptive shearlet-regularized iterative image deblurring algorithm, where the image decon-volution problem is solved through the alternating direction method of multipliers (ADMM). As the discrepancy principle is employed, the regularization parameter can be refreshed with a closed form adaptively in each iteration. Numerical simulation results of image deblurring problems are presented to illustrate the effectiveness of the proposed method in terms of both detail preservation and speed.