Gabor Analysis for Imaging

  • Ole Christensen
  • Hans G. Feichtinger
  • Stephan Paukner


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...


Tight Frame Dual Frame Gabor Frame Separable Lattice Frame Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ole Christensen
    • 1
  • Hans G. Feichtinger
    • 2
  • Stephan Paukner
    • 3
  1. 1.Technical University of DenmarkLyngbyDenmark
  2. 2.University of ViennaViennaAustria
  3. 3.Applied Research Center Communication Systems GmbHViennaAustria

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