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A Nonlinear Multigrid Method for Total Variation Minimization from Image Restoration

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Abstract

Image restoration has been an active research topic and variational formulations are particularly effective in high quality recovery. Although there exist many modelling and theoretical results, available iterative solvers are not yet robust in solving such modeling equations. Recent attempts on developing optimisation multigrid methods have been based on first order conditions. Different from this idea, this paper proposes to use piecewise linear function spanned subspace correction to design a multilevel method for directly solving the total variation minimisation. Our method appears to be more robust than the primal-dual method (Chan et al., SIAM J. Sci. Comput. 20(6), 1964–1977, 1999) previously found reliable. Supporting numerical results are presented.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool, L69 7ZL, UK

    Ke Chen

  2. Department of Mathematics, University of Bergen, Bergen, Norway

    Xue-Cheng Tai

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  1. Ke Chen
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  2. Xue-Cheng Tai
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Correspondence to Ke Chen.

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Chen, K., Tai, XC. A Nonlinear Multigrid Method for Total Variation Minimization from Image Restoration. J Sci Comput 33, 115–138 (2007). https://doi.org/10.1007/s10915-007-9145-9

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