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Combining the discrete wavelet transform and mixed-domain filtering.

M S Lazar1, L T Bruton

  • 1Dept. of Electr. and Comput. Eng., Calgary Univ., Alta.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 1, 1996
PubMed
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A new filtering method combines discrete orthogonal wavelet transform (DWT) with mixed-domain (mixed-D) filtering for signal processing. This approach enhances subband coding systems by enabling selective filtering of signal spectra, as demonstrated in video processing applications.

Area of Science:

  • Signal Processing
  • Image and Video Processing
  • Applied Mathematics

Background:

  • Traditional filtering methods often face challenges in efficiently processing multi-dimensional signals.
  • Mixed-domain (mixed-D) filtering offers a flexible approach but can be complex to optimize for specific spectral characteristics.
  • Discrete orthogonal wavelet transform (DWT) provides effective signal decomposition and spectral partitioning capabilities.

Purpose of the Study:

  • To introduce a novel filtering technique integrating DWT with mixed-D filtering.
  • To leverage DWT for pre- and post-processing within the mixed-D filtering framework.
  • To demonstrate the applicability of the combined method in subband coding and video processing.

Main Methods:

  • The proposed method utilizes DWT to decompose the signal into subbands before and after mixed-D filtering.

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  • DWT facilitates controlled spectral partitioning, allowing selective filtering of specific frequency bands.
  • The core of the filtering process employs linear difference equations (LDE) within the mixed-D algorithm.

    • Main Results:

    • The integration of DWT with ideal high- and low-pass filters does not alter the fundamental LDE filters used in mixed-D filtering.
    • DWT modifies the frequency tuple associated with each LDE filter, enabling subband-specific processing.
    • The filtering of a three-dimensional linear trajectory signal, a common video processing task, was successfully demonstrated.

    Conclusions:

    • The combined DWT-mixed-D filtering method offers a robust and adaptable approach for signal processing.
    • The technique is well-suited for integration into subband coding systems due to its spectral control.
    • The successful application to 3-D trajectory signal filtering highlights its practical utility in video analysis.