## 6 Discussion and Conclusions  
In this work, we study a new regularization model by applying TV with OGS and Lp-pseudo-norm shrinkage for the image polluting under impulse noise. We provided the efficient algorithm OGS-Lp-FAST under the ADMM framework. This algorithm is rooted in overlapping group sparsity-based regularization, and incorporated the comparisons made with ATV, ITV, TGV, OGS-L1, and OGS-Lp models for validation of our proposed method. The following conclusions are drawn from the experimental results:  
Figure 6: Comparison of image details recovered by our proposed models and other models. The test images (“Woman”, “Pepper”, “Girl”, and “House”) are corrupted by 20–50% impulse noise, respectively.  
An overlapping group sparsity (OGS)-based regularizer is used to replace the anisotropic total variation (ATV), to describe the prior conditions of the image. OGS makes full use of the similarity among image neighborhoods and the dissimilarity in the surroundings of each point. It promotes the distinction between the smooth and edge regions of an image, thus enhancing the robustness of the proposed model.
2. Lp-pseudo-norm shrinkage is used in place of the L1-norm regularization to describe the fidelity term of images with salt and pepper noise. With the inclusion of another degree of freedom, Lp-pseudo-norm shrinkage reflects the sparsity of the image better and greatly improves the denoising performance of the algorithm.
3. The difference operator is used for convolution. Under the ADMM framework, the complex model is transformed into a series of simpler mathematical problems to solve.
4. Appropriate K values could effectively improve the overall denoising performance of the model. In practice, this parameter needs to be adjusted. If it is too small, the neighborhood information is not utilized completely. If the value is too big, too many dissimilar pixel blocks will be included, impairing the denoising result.
5. The adoption of accelerated ADMM with a restart accelerates the convergence of the algorithm. The running time is reduced.
6. In this paper, we focus on impulse noise removal, but the model is also applicable to other types of noise removal that we will further study in future work.  
Funding acquisition, F.Y.; Methodology, L.W., Y.C. ([PERSON]) and F.L.; Software, L.W., Y.C. ([PERSON]) and Y.C. ([PERSON]) and Z.C.; Writing--original draft, L.W.; Writing--review & editing, Y.C. ([PERSON]).  
This work is supported by the Foundation of Fujian Province Great Teaching Reform [FBJG20180015]. the Education and Scientific Research Foundation of Education Department of Fujian Province for Middle-aged and Young Teachers [grant number JT180309],the Education and Scientific Research Foundation of Education Department of Fujian Province for Middle-aged and Young Teachers [grant number JAT170352], the Foundation of Department of Education of Guangdong Province [2017 KCXTD015], and the Open Foundation of Digital Signal and Image Processing Key Laboratory of Guangdong Province [grant number 2017 GCDSIPL-01], the Education and Scientific Research Foundation of Education Department of Fujian Province for Middle-aged and Young Teachers [grant number JT180310], the Education and Scientific Research Foundation of Education Department of Fujian Province for Middle-aged and Young Teachers [grant number JT180311].  
The authors declare no conflict of interest.