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Sparsity Regularization for Radon Measures

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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))

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Abstract

In this paper we establish a regularization method for Radon measures. Motivated from sparse L 1 regularization we introduce a new regularization functional for the Radon norm, whose properties are then analyzed. We, furthermore, show well-posedness of Radon measure based sparsity regularization. Finally we present numerical examples along with the underlying algorithmic and implementation details. We shall, here, see that the number of iterations turn out of utmost importance when it comes to obtain reliable reconstructions of sparse data with varying intensities.

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Authors and Affiliations

  1. Department of Mathematics, University of Innsbruck, Technikerstr. 21a, A-6020, Innsbruck, Austria

    Otmar Scherzer & Birgit Walch

  2. Radon Institute of Computational and Applied Mathematics, Altenberger Str. 69, A-4040, Linz, Austria

    Otmar Scherzer

Authors
  1. Otmar Scherzer
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  2. Birgit Walch
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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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© 2009 Springer-Verlag Berlin Heidelberg

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Scherzer, O., Walch, B. (2009). Sparsity Regularization for Radon Measures. 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_38

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  • DOI: https://doi.org/10.1007/978-3-642-02256-2_38

  • 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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