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The generalized Gabor transform.

J Yao1, P Krolak, C Steele

  • 1Digital Equipment Corp., Nashua, NH.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 1, 1995
PubMed
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This study introduces the generalized Gabor transform for image representation, detailing its computation using optimal biorthogonal functions. Efficient algorithms are proposed for both continuous and finite discrete cases, enhancing signal processing capabilities.

Area of Science:

  • Signal Processing
  • Image Representation
  • Mathematical Physics

Background:

  • The original Gabor transform (1946) is a special case of the generalized Gabor transform.
  • The generalized Gabor transform decomposes functions into coefficients using a specific mathematical formulation.
  • Biorthogonal functions are crucial for accurately computing the generalized Gabor transform.

Purpose of the Study:

  • To discuss the computation of the generalized Gabor transform using biorthogonal functions.
  • To present the relationship between window functions and their optimal biorthogonal counterparts.
  • To derive and propose efficient algorithms for the finite discrete generalized Gabor transform.

Main Methods:

  • Utilizing the Zak transform (1967) to establish a relation between window functions and optimal biorthogonal functions for rational T/T' ratios.

Related Experiment Videos

  • Deriving the finite discrete version of the generalized Gabor transform.
  • Developing and proposing efficient computational algorithms for optimal biorthogonal functions and the transform itself.

    • Main Results:

    • A method for computing the generalized Gabor transform with optimal biorthogonal functions is presented.
    • A relationship between window functions and their optimal biorthogonal functions is established using the Zak transform.
    • Efficient algorithms for the finite discrete generalized Gabor transform and its associated optimal biorthogonal functions are proposed.

    Conclusions:

    • The generalized Gabor transform offers a flexible framework for image representation.
    • Optimal biorthogonal functions are key to efficient and accurate computation.
    • The proposed algorithms enhance the practical application of the generalized Gabor transform in signal processing.