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Pseudo-Differential Operators, Microlocal Analysis and Image Restoration

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Advances in Pseudo-Differential Operators

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 155))

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Abstract

Pseudo-differential operators with symbols supported on sectors of dyadic annuli in the Fourier domain are used to perform microlocal analysis of tempered distributions. Microlocal analysis is recalled. The above symbols are made of smooth wavelet frames which are constructed in the Fourier domain by means of modulated smooth tapered functions. The method is used to localize a line of singularities in an image.

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Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, Osaka Kyoiku University, Kashiwara, Osaka, 582-8582, Japan

    Ryuichi Ashino

  2. Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave, Ottawa, 6N5, ON, Canada

    J. Steven Desjardins

  3. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Chris Heil

  4. Department of Mathematics Graduate School of Science, Osaka University, Osaka, 560-0043, Japan

    Michihiro Nagase

  5. Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave, Ottawa, 6N5, Canada

    Rémi Vaillancourt

Authors
  1. Ryuichi Ashino
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  2. J. Steven Desjardins
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  3. Chris Heil
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  4. Michihiro Nagase
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  5. Rémi Vaillancourt
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Editor information

Editors and Affiliations

  1. Division of Mathematical Sciences, Osaka Kyoiku University, Kashiwara, Osaka, 582-8582, Japan

    Ryuichi Ashino

  2. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto, 10, Torino, 10123, Italy

    Paolo Boggiatto

  3. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada

    M. W. Wong

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© 2004 Springer Basel AG

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Ashino, R., Desjardins, J.S., Heil, C., Nagase, M., Vaillancourt, R. (2004). Pseudo-Differential Operators, Microlocal Analysis and Image Restoration. In: Ashino, R., Boggiatto, P., Wong, M.W. (eds) Advances in Pseudo-Differential Operators. Operator Theory: Advances and Applications, vol 155. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7840-1_11

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  • DOI: https://doi.org/10.1007/978-3-0348-7840-1_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9590-3

  • Online ISBN: 978-3-0348-7840-1

  • eBook Packages: Springer Book Archive

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