Poissonian image deblurring method by non-local total variation and framelet regularization constraint

Total variation is often used to exploit the gradient sparsity for its ability of suppressing noise and preserving edges. But it may also smooth out the edges and details due to its piecewise constant solution which introduces staircase effect into the deblurring results. Thus, how to choose a good regularization constraint is really important, which, however, is still a challenging research topic. To address this problem, we consider a non-local constraint term instead of the local constraint term in hope of exploiting the self-similarity of non-local image patches. Furthermore, a framelet-based regularization constraint is introduced into the proposed deblurring model to explore the image sparsity and preserve the structure information of different scales. Split Bregman technique is used to solve the joint optimization problem of the proposed model. Experimental results demonstrate the efficiency of the proposed method in terms of the visual perception and the normalized mean square error. (C) 2016 Elsevier Ltd. All rights reserved.