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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.

Non-Convex High Order Total Variation With Overlapping Group Sparsity Denoising Model Under Cauchy Noise