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Stability and Instability in Discrete Tomography

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Digital and Image Geometry

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2243))

Abstract

The paper gives strong instability results for a basic reconstruction problem of discrete tomography, an area that is particularly motivated by demands from material sciences for the reconstruction of crystalline structures from images produced by quantitative high resolution transmission electron microscopy. In particular, we show that even extremely small changes in the data may lead to entirely different solutions. We will also give some indication of how one can possibly handle the ill-posedness of the reconstruction problem in practice.

Supported in part by the German Federal Ministry of Education and Research Grant 03-GR7TM1.

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Author information

Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Arcisstr. 21, D-80290, München, Germany

    Andreas Alpers

  2. Zentrum Mathematik, Technische Universität München, Arcisstr. 21, D-80290, München, Germany

    Peter Gritzmann

  3. tfk GmbH, Baierbrunner Str.39, D-81379, München, Germany

    Lionel Thorens

Authors
  1. Andreas Alpers
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  2. Peter Gritzmann
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  3. Lionel Thorens
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Editor information

Editors and Affiliations

  1. Groupe ESIEE, Cité Descartes, 2, Bld. Blaise-Pascal, 93162, Noisy-le-Grand, France

    Gilles Bertrand

  2. Media Technology Division, Chiba University, Inst. of Media and Information Technology, 1-33 Yayoi-cho, Inage-ku, 263-8522, Chiba, Japan

    Atsushi Imiya

  3. The University of Auckland, CITR Tamaki, Tamaki Campus, Morrin Road, Glen Innes, 1005, Auckland, New Zealand

    Reinhard Klette

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© 2001 Springer-Verlag Berlin Heidelberg

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Alpers, A., Gritzmann, P., Thorens, L. (2001). Stability and Instability in Discrete Tomography. In: Bertrand, G., Imiya, A., Klette, R. (eds) Digital and Image Geometry. Lecture Notes in Computer Science, vol 2243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45576-0_11

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  • DOI: https://doi.org/10.1007/3-540-45576-0_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43079-7

  • Online ISBN: 978-3-540-45576-9

  • eBook Packages: Springer Book Archive

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