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Signal and image approximation using interval wavelet transform.

Wei Siong Lee1, Ashraf A Kassim

  • 1Department of Electrical and Computer Engineering, National University of Singapore. eleleews@nus.edu.sg

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 8, 2007
PubMed
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Classical wavelet transforms create artifacts near signal breaks. New interval wavelet methods avoid this, offering sparser representations for improved image compression and upscaling.

Area of Science:

  • Signal Processing
  • Image Analysis
  • Applied Mathematics

Background:

  • Classical wavelet transforms can introduce Gibbs-like artifacts around signal discontinuities due to coefficient quantization.
  • These artifacts arise when wavelet coefficients within the cone of influence of discontinuities are affected.

Purpose of the Study:

  • To introduce novel interval wavelet constructions.
  • To demonstrate the utility of these interval wavelets for image compression and upscaling.
  • To overcome limitations of classical wavelet synthesis in representing discontinuous signals.

Main Methods:

  • Analyzing functions in a piecewise manner to avoid filtering across discontinuities.
  • Developing two new interval wavelet constructions.
  • Applying interval wavelet transforms to generate sparser signal representations near discontinuities.

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Main Results:

  • Interval wavelet transforms generate sparser representations in the vicinity of discontinuities compared to classical methods.
  • The proposed interval wavelet constructions effectively mitigate Gibbs-like phenomena.
  • Demonstrated successful application in image compression and upscaling tasks.

Conclusions:

  • Piecewise function analysis enables filtering avoidance, leading to improved signal representation.
  • New interval wavelets offer a superior alternative for handling discontinuities in signal processing.
  • The developed methods show promise for enhanced image compression and upscaling applications.