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Gabor Analysis for Imaging

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Handbook of Mathematical Methods in Imaging

Introduction

In contrast to classical Fourier analysis, time-frequency analysis is concerned with localized Fourier transforms. Gabor analysis is an important branch of time-frequency analysis. Although significantly different, it shares with the wavelet transform methods the ability to describe the smoothness of a given function in a location-dependent way.

The main tool is the sliding window Fourier transform or short-time Fourier transform (STFT) in the context of audio signals. It describes the correlation of a signal with the time-frequency shifted copies of a fixed function (or window, or atom). Thus, it characterizes a function by its transform over phase space, which is the time-frequency plane (TF-plane) in a musical context, or the location-wavenumber-domain in the context of image processing.

Since the transition from the signal domain to the phase space domain introduces an enormous amount of data redundancy, suitable subsampling of the continuous transform allows for...

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Author information

Authors and Affiliations

  1. Technical University of Denmark, Lyngby, Denmark

    Ole Christensen

  2. University of Vienna, Vienna, Austria

    Hans G. Feichtinger

  3. Applied Research Center Communication Systems GmbH, Vienna, Austria

    Stephan Paukner

Authors
  1. Ole Christensen
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  2. Hans G. Feichtinger
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  3. Stephan Paukner
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Editors and Affiliations

  1. Computational Science Center, University of Vienna, Nordbergstrasse 15, Vienna, Austria

    Otmar Scherzer

  2. RICAM, Austrian Academy of Sciences, Linz, Austria

    Otmar Scherzer

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Christensen, O., Feichtinger, H.G., Paukner, S. (2011). Gabor Analysis for Imaging. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-0-387-92920-0_29

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