5. Discrete Wavelet Transform

  1. Tinku Acharya and
  2. Ajoy K. Ray

Published Online: 20 SEP 2005

DOI: 10.1002/0471745790.ch5

Image Processing: Principles and Applications

Image Processing: Principles and Applications

How to Cite

Acharya, T. and Ray, A. K. (2005) Discrete Wavelet Transform, in Image Processing: Principles and Applications, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471745790.ch5

Publication History

  1. Published Online: 20 SEP 2005
  2. Published Print: 19 AUG 2005

ISBN Information

Print ISBN: 9780471719984

Online ISBN: 9780471745792

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Keywords:

  • wavelet;
  • dilation;
  • translation;
  • discrete wavelet transform;
  • DWT;
  • multiresolution analysis;
  • pyramid algorithm;
  • lifting;
  • primal and dual lifting

Summary

The Discrete Wavelet Transform (DWT) became a very versatile signal processing tool after Mallat proposed the multi-resolution representation of signals based on wavelet decomposition. Wavelets allow both time and frequency analysis of signals simultaneously because of the fact that the energy of wavelets is concentrated in time and still possesses the wave-like (periodic) characteristics. As a result, wavelet representation provides a versatile mathematical tool to analyze transient, time-variant (non-stationary) signals that are not statistically predictable especially at the region of discontinuities – a feature that is typical of images having discontinuities at the edges. The DWT decomposes a digital signal into different subbands so that the lower frequency subbands have finer frequency resolution and coarser time resolution compared to the higher frequency subbands. DWT is the basis of the new JPEG2000 image compression standard. In this chapter, we have covered the principles behind wavelet transformation, the concept of multiresolution analysis and pyramid algorithm for finite impulse response filter implementation of DWT. We have also discussed the foundations and principles behind computationally efficient “lifting” implementation of DWT in great detail in this chapter along with some examples.