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Domain Decomposition Methods for Total Variation Minimization

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8932))

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Abstract

In this paper, overlapping domain decomposition methods (DDMs) are used for solving the Rudin-Osher-Fatemi (ROF) model in image restoration. It is known that this problem is nonlinear and the minimization functional is non-strictly convex and non-differentiable. Therefore, it is difficult to analyze the convergence rate for this problem. In this work, we use the dual formulation of the ROF model in connection with proper subspace correction. With this approach, we overcome the problems caused by the non-strict-convexity and non-differentiability of the ROF model. However, the dual problem has a global constraint for the dual variable which is difficult to handle for subspace correction methods. We propose a stable unit decomposition, which allows us to construct the successive subspace correction method (SSC) and parallel subspace correction method (PSC) based domain decomposition. Numerical experiments are supplied to demonstrate the efficiency of our proposed methods.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Tianjin Normal University, Tianjin, P.R. China

    Huibin Chang

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

    Xue-Cheng Tai

  3. Department of Mathematics, East China Normal University, Shanghai, P.R. China

    Danping Yang

Authors
  1. Huibin Chang
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  2. Xue-Cheng Tai
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  3. Danping Yang
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, 7800, Bergen, Norway

    Xue-Cheng Tai

  2. Department of Mathematics, University of California, Los Angeles, CA, USA

    Egil Bae

  3. The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, S.A.R.

    Tony F. Chan

  4. Telemark University College, Postboks 203, 3901, Porsgrunn, Norway

    Marius Lysaker

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© 2015 Springer International Publishing Switzerland

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Chang, H., Tai, XC., Yang, D. (2015). Domain Decomposition Methods for Total Variation Minimization. In: Tai, XC., Bae, E., Chan, T.F., Lysaker, M. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2015. Lecture Notes in Computer Science, vol 8932. Springer, Cham. https://doi.org/10.1007/978-3-319-14612-6_25

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  • DOI: https://doi.org/10.1007/978-3-319-14612-6_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14611-9

  • Online ISBN: 978-3-319-14612-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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