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A nonconvex and nonsmooth anisotropic total variation model for image noise and blur removal

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Abstract

In this paper, a nonconvex and nonsmooth anisotropic total variation model is proposed, which can provide a very sparser representation of the derivatives of the function in horizontal and vertical directions. The new model can preserve sharp edges and alleviate the staircase effect often arising in total variation (TV) based models. We use graduated nonconvexity (GNC) algorithm to solve the proposed nonconvex and nonsmooth minimization problem. Starting with a convex initialization, it uses a family of nonconvex functional to gradually approach the original nonconvex functional. For each subproblem, we use function splitting technique to separately address the nonconvex and nonsmooth properties, and use augmented Lagrangian method (ALM) to solve it. Experiments are conducted for both synthetic and real images to demonstrate the effectiveness of the proposed model. In addition, we compare it with several state-of-the-art models in denoising and deblurring applications. The numerical results show that our model has the best performance in terms of PSNR and MSSIM indexes.

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Acknowledgments

This work was supported in part by the Natural Science Foundation of China under Grant No. 61561019, and the Doctoral Scientific Fund Project of Hubei University for Nationalities under Grant No. MY2015B001.

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  1. School of Science, Hubei Minzu University, Enshi, 445000, People’s Republic of China

    Yanjun Ren & Liming Tang

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  1. Yanjun Ren
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Correspondence to Liming Tang.

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Ren, Y., Tang, L. A nonconvex and nonsmooth anisotropic total variation model for image noise and blur removal. Multimed Tools Appl 79, 1445–1473 (2020). https://doi.org/10.1007/s11042-019-08179-8

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