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Augmented Lagrangian Method for Generalized TV-Stokes Model

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Abstract

In this paper, we propose a general form of TV-Stokes models and provide an efficient and fast numerical algorithm based on the augmented Lagrangian method. The proposed model and numerical algorithm can be used for a number of applications such as image inpainting, image decomposition, surface reconstruction from sparse gradient, direction denoising, and image denoising. Comparing with properties of different norms in regularity term and fidelity term, various results are investigated in applications. We numerically show that the proposed model recovers jump discontinuities of a data and discontinuities of the data gradient while reducing stair-case effect.

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria

    Jooyoung Hahn

  2. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Chunlin Wu & Xue-Cheng Tai

  3. Mathematics Institute, University of Bergen, Bergen, Norway

    Xue-Cheng Tai

Authors
  1. Jooyoung Hahn
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  2. Chunlin Wu
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  3. Xue-Cheng Tai
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Correspondence to Jooyoung Hahn.

Additional information

The research is supported by MOE (Ministry of Education) Tier II project T207N2202 and IDM project NRF2007IDMIDM002-010.

Jooyoung Hahn, who is currently at Institute of Mathematics and Scientific Computing in University of Graz, Austria, has been supported by the Austrian Science Fund (FWF) under the START-Program Y305 “Interfaces and Free Boundaries” and the SFB “Mathematical Optimization and Its Applications in Biomedical Sciences” since November 2010.

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Hahn, J., Wu, C. & Tai, XC. Augmented Lagrangian Method for Generalized TV-Stokes Model. J Sci Comput 50, 235–264 (2012). https://doi.org/10.1007/s10915-011-9482-6

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  • DOI: https://doi.org/10.1007/s10915-011-9482-6

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