A combined non-convex TVp and wavelet \(\ell _1\)-norm approach for image deblurring via split Bregman method

Image deblurring is one of the most fundamental problems in the image processing and computer vision fields. The methods based on total variation are effective for image deblurring because it is able to preserve sharp edges, which are usually the most important parts of an image. However, these methods usually produce undesirable staircase artifacts. In order to alleviate the staircase effects, in this paper we propose an effective scheme for image deblurring based on the TVp regularization and wavelet frame. The new model combines the advantages of nonconvex regularization and wavelet frame based method, and it can well remove the blur and noise while preserving the valuable edges and contours of the image. To solve the proposed model, we develop a fast minimization algorithm under the framework of the split Bregman algorithm and further apply Nesterov acceleration technique to improve the convergence speed. The results from peak signal-to-noise ratio and structural similarity index measurements show the effectiveness of our proposed method when compared to previous state-of-the-art methods for image deblurring.