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Non-Overlapping Domain Decomposition Methods For Dual Total Variation Based Image Denoising

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Abstract

In this paper non-overlapping domain decomposition methods for the pre-dual total variation minimization problem are introduced. Both parallel and sequential approaches are proposed for these methods for which convergence to a minimizer of the original problem is established. The associated subproblems are solved by a semi-smooth Newton method. Several numerical experiments are presented, which show the successful application of the sequential and parallel algorithm for image denoising.

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Authors and Affiliations

  1. Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 , Berlin, Germany

    Michael Hintermüller

  2. Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, 8010 , Graz, Austria

    Andreas Langer

Authors
  1. Michael Hintermüller
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  2. Andreas Langer
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Corresponding author

Correspondence to Andreas Langer.

Additional information

This work was supported by the Austrian Science Fund FWF through the START Project Y 305-N18 “Interfaces and Free Boundaries” and the SFB Project F32 04-N18 “Mathematical Optimization and Its Applications in Biomedical Sciences”

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Hintermüller, M., Langer, A. Non-Overlapping Domain Decomposition Methods For Dual Total Variation Based Image Denoising. J Sci Comput 62, 456–481 (2015). https://doi.org/10.1007/s10915-014-9863-8

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  • DOI: https://doi.org/10.1007/s10915-014-9863-8

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