Hybrid regularization image deblurring in the presence of impulsive noise

•We propose a new model for restoring images corrupted by blur and impulse noise.•The proposed model suppress the staircasing-artifacts caused by TV-based methods.•We propose a efficient algorithm to solve this proposed model.•Numerical examples are presented to compare the proposed method with TV-L1L1 approach.

Image deblurring is one of the fundamental problems in the image processing and computer vision fields. In this paper, we propose a new approach for restoring images corrupted by blur and impulse noise. The existing methods used to address this problem are based on minimizing the objective functional, which is the sum of the L1L1-data fidelity term, and the total variation (TV) regularization term. However, TV introduces staircase effects. Thus, we propose a new objective functional that combines the tight framelet and TV to restore images corrupted by blur and impulsive noise while mitigating staircase effects. The minimization of the new objective functional presents a computational challenge. We propose a fast minimization algorithm by employing the augmented Lagrangian technique. The experiments on a set of image deblurring benchmark problems show that the proposed method outperforms previous state-of-the-art methods for image restoration.