Research on image deblurring based on second order total variation and Lp pseudo-norm

Anisotropic total variation (ATV) regularization is widely used in image deblurring applications. However, the traditional ATV model suffers from at least two limitations. Firstly, the traditional ATV model assumes the image to be piecewise constant and only considers the sparsity of the first-order image gradients, resulting in staircase artifacts. Secondly, the traditional ATV model employs the L1-norm to depict the sparsity of image gradients. Nonetheless, the L1-norm has a limited capability of depicting the sparsity of sparse variables. To overcome the two challenges, a new deblurring model is presented via the second-order gradient sparse constraint and Lp-pseudo-norm shrinkage. The second-order total variation is incorporated for fitting the image prior term and relieving the staircase artifacts. The Lp-pseudo-norm shrinkage is employed to depict sparse variables precisely. The alternating direction method of multipliers is employed to decompose the presented model into several decoupled subproblems. Finally, experiments are carried out to show the performance of the proposed method. The results show that the proposed method outperforms the other deblurring models mentioned in this article.