Weighted-l1-method-noise regularization for image deblurring

Abstract Various image prior based regularization techniques have been proposed for image deblurring. By utilizing existing image smoothing operators, the method-noise provides a new way to formulate image regularizers. The method noise is defined as the difference of an image and its smoothed version, obtained by an image smoothing operator such as the non-local means(NLM). Therefore, the method noise mainly contains edges, small scaled details and noise (if exists). The l2-NLM method noise regularization has been successfully used in image denoising. However, the restored image exists over-smoothed edges and noise in smooth areas cannot be perfectly removed. In this work, we propose a weighted-l1-method-noise regularization model for image deblurring. We analyze the advantages of the proposed model in terms of variational form and its solution. Specifically, the l1 penalty of the method noise is better than the l2 penalty in removing noise in smooth areas. The incorporated gradient based weight can better preserve image edges. Experimental results show that the proposed method can obtain better results than other method noise based regularization methods.