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It is widely known that the total variation regularization model preserves the edges well in the restored images but has some staircase effects. We consider using non-convex high-order total variation and overlapping group sparsity as a hybrid regularization to present a new denoising model. The proposed model can well preserve edges and reduce the staircase effect in the smooth region of the restored images. In order to solve the proposed hybrid model, we develop an efficient alternating minimization method. Compared with other models for removing Cauchy noise, numerical experimental results demonstrate that the superiority of the proposed model and algorithm, both in terms of visual and quantitative measures. INDEX TERMSNon-convex high-order total variation; Overlapping group sparsity; Cauchy noise VOLUME xx, xxxx

In recent years, the fractional-order derivative has achieved great success in removing Gaussian noise, impulsive noise, multiplicative noise and so on, but few works have been conducted to remove Cauchy noise. In this paper, we propose a novel nonconvex variational model for removing Cauchy noise based on the truncated fractional-order total variation. The new model can effectively reduce the staircase effect and keep small details or textures while removing Cauchy noise. In order to solve the nonconvex truncated fractional-order total variation regularization model, we propose an efficient alternating minimization method under the framework of the alternating direction multiplier method. Experimental results illustrate the effectiveness of the proposed model, compared to some previous models.