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Dual-Primal Domain Decomposition Methods for the Total Variation Minimization

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Domain Decomposition Methods in Science and Engineering XXIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 116))

Abstract

We propose nonoverlapping domain decomposition methods for solving the total variation minimization problem. We decompose the domain of the dual problem into nonoverlapping rectangular subdomains, where local total variation problems are solved. We convert the local dual problems into the equivalent primal forms which reproduce the original problem at smaller dimension. Sequential and parallel algorithms are presented. The convergence of both algorithms is analyzed and numerical results are presented.

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Authors and Affiliations

  1. Department of Mathematical Sciences, KAIST, Daejeon, 34141, South Korea

    Chang-Ock Lee & Changmin Nam

Authors
  1. Chang-Ock Lee
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  2. Changmin Nam
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Corresponding author

Correspondence to Changmin Nam .

Editor information

Editors and Affiliations

  1. Dept. of Mathematical Sciences, KAIST, Daejeon, Korea (Republic of)

    Chang-Ock Lee

  2. Dept. of Computer Science, University of Colorado, Boulder, Colorado, USA

    Xiao-Chuan Cai

  3. Applied Math & Computational Science, KAUST, Thuwal, Saudi Arabia

    David E. Keyes

  4. Dept. of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. Mathematisches Institut, Universität zu Köln, Köln, Germany

    Axel Klawonn

  6. Dept. of Computational Science & Engineering, Yonsei University, Seoul, Korea (Republic of)

    Eun-Jae Park

  7. Courant Institute of Mathematical Sciences, New York University, New York, New York, USA

    Olof B. Widlund

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Lee, CO., Nam, C. (2017). Dual-Primal Domain Decomposition Methods for the Total Variation Minimization. In: Lee, CO., et al. Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-52389-7_38

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