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Nonlinear multigrid method for solving the anisotropic image denoising models

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Abstract

In this paper, we study a nonlinear multigrid method for solving a general image denoising model with two L 1-regularization terms. Different from the previous studies, we give a simpler derivation of the dual formulation of the general model by augmented Lagrangian method. In order to improve the convergence rate of the proposed multigrid method, an improved dual iteration is proposed as its smoother. Furthermore, we apply the proposed method to the anisotropic ROF model and the anisotropic LLT model. We also give the local Fourier analysis (LFAs) of the Chambolle’s dual iterations and a modified smoother for solving these two models, respectively. Numerical results illustrate the efficiency of the proposed method and indicate that such a multigrid method is more suitable to deal with large-sized images.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, Hunan, China

    Jun Zhang

  2. Department of Information and Computing Science, Changsha University, Changsha, 410003, Hunan, China

    Yu-Fei Yang

Authors
  1. Jun Zhang
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  2. Yu-Fei Yang
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Corresponding author

Correspondence to Yu-Fei Yang.

Additional information

The research has been supported by the NNSF of China (Nos. 60872129 and 60835004) and the Major Project of Ministry of Education of China (No. 309023).

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Zhang, J., Yang, YF. Nonlinear multigrid method for solving the anisotropic image denoising models. Numer Algor 63, 291–315 (2013). https://doi.org/10.1007/s11075-012-9623-5

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  • DOI: https://doi.org/10.1007/s11075-012-9623-5

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