By combining with the shearlet transform and the second-order total generalized variation (TGV) regularization, a strictly convex shearlet-TGV based model is proposed for restoring images corrupted by Cauchy noise. The shearlet-TGV based model can be taken as a minimization problem for which the objective function is composed of a second-order TGV regularization term, a \(l_{1}\)-norm to the shearlet transform, a data fidelity term to the Cauchy noise, and a quadratic penalty term to guarantee the uniqueness of the solution. Computationally, the shearlet-TGV based model is transformed into a minimax problem by using the dual technique of optimization. Then, a high efficient Chambolle–Pock’s first-order primal–dual algorithm is developed to solve the transformed minimax problem. At last, compared with several existing state-of-the-art methods, experimental results demonstrate the effectiveness of our proposed method, in terms of the signal to noise ratio, the peak signal to noise ratio, the mean square error and the structural similarity index.

通过结合剪切波变换和二阶总广义变异（TGV）正则化，提出了一种基于严格凸剪切波TGV的模型，用于恢复柯西噪声所破坏的图像。基于剪切波TGV的模型可以看作是一个最小化问题，其目标函数由二阶TGV正则项\（l_ {1} \）组成-对Sletlet变换进行范数化，对Cauchy噪声进行数据保真度检验，并采用二次罚分法来保证解的唯一性。在计算上，通过使用对偶优化技术，将基于Slicelet-TGV的模型转换为极小极大问题。然后，开发了一种高效的Chambolle-Pock的一阶原始对偶算法来解决变换后的极大极小问题。最后，与几种现有的最新技术相比，实验结果证明了我们提出的方法的有效性，无论是在信噪比，峰值信噪比，均方误差和结构相似性方面指数。