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Multidimensional, mapping-based complex wavelet transforms.

Felix C A Fernandes1, Rutger L C van Spaendonck, C Sidney Burrus

  • 1Texas Instruments, Inc., Dallas, TX 75235, USA. felixf@ti.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 14, 2005
PubMed
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New complex wavelet transforms overcome discrete wavelet transform limitations like shift sensitivity and poor directionality. These advanced transforms offer improved signal processing, especially for seismic data, achieving state-of-the-art results.

Area of Science:

  • Signal Processing
  • Image Processing
  • Applied Mathematics

Background:

  • Discrete Wavelet Transform (DWT) is widely used but suffers from shift sensitivity, poor directionality, and lack of phase information.
  • Existing transforms mitigating DWT shortcomings often introduce redundancy or lack desired properties.

Purpose of the Study:

  • To introduce novel multidimensional, mapping-based complex wavelet transforms.
  • To address the limitations of DWT, specifically shift sensitivity, directionality, and phase information.
  • To develop a directional, nonredundant complex wavelet transform and a shift-insensitive, directional, complex wavelet transform with low redundancy.

Main Methods:

  • A mapping onto a complex function space followed by a DWT of the complex mapping.
  • Decoupled implementation allowing controllable redundancy and flexibility in DWT choice.

Related Experiment Videos

  • Development of the complex double-density DWT as an example.

    • Main Results:

    • A directional, nonredundant complex wavelet transform was created, offering benefits for image coding.
    • A shift-insensitive, directional, complex wavelet transform with low redundancy was developed.
    • State-of-the-art results were demonstrated in seismic signal-processing applications.

    Conclusions:

    • Multidimensional, mapping-based complex wavelet transforms effectively overcome DWT limitations.
    • The proposed transforms offer a unique combination of directionality, nonredundancy, and shift-insensitivity.
    • These advanced transforms show significant potential for enhancing signal processing applications, particularly in seismology.