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

  • Yanjun Ren
  • Liming TangEmail author
Article
  • 16 Downloads

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.

Keywords

Total variation Nonconvex Nonsmooth Anisotropic total variation Graduated nonconvexity algorithm 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of ScienceHubei Minzu UniversityEnshiPeople’s Republic of China

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