Shearlet-TGV based model for restoring noisy images corrupted by Cauchy noise

Abstract

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.