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Nonlocal Variational Image Deblurring Models in the Presence of Gaussian or Impulse Noise

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Scale Space and Variational Methods in Computer Vision (SSVM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5567))

Abstract

We wish to recover an image corrupted by blur and Gaussian or impulse noise, in a variational framework. We use two data-fidelity terms depending on the noise, and several local and nonlocal regularizers. Inspired by Buades-Coll-Morel, Gilboa-Osher, and other nonlocal models, we propose nonlocal versions of the Ambrosio-Tortorelli and Shah approximations to Mumford-Shah-like regularizing functionals, with applications to image deblurring in the presence of noise. In the case of impulse noise model, we propose a necessary preprocessing step for the computation of the weight function. Experimental results show that these nonlocal MS regularizers yield better results than the corresponding local ones (proposed for deblurring by Bar et al.) in both noise models; moreover, these perform better than the nonlocal total variation in the presence of impulse noise. Characterization of minimizers is also given.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095-1555, USA

    Miyoun Jung & Luminita A. Vese

Authors
  1. Miyoun Jung
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  2. Luminita A. Vese
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008, Bergen, Norway

    Xue-Cheng Tai

  2. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Oslo, Norway

    Knut Mørken

  3. Simula Research Laboratory, M. Linges v 17, Fornebu, P.O.Box 134, N-1325, Lysaker, Norway

    Marius Lysaker

  4. SINTEF ICT, Oslo, Norway

    Knut-Andreas Lie

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Jung, M., Vese, L.A. (2009). Nonlocal Variational Image Deblurring Models in the Presence of Gaussian or Impulse Noise. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_34

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  • DOI: https://doi.org/10.1007/978-3-642-02256-2_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02255-5

  • Online ISBN: 978-3-642-02256-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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