Computational Complexity

2012 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Wavelets, Introduction to

  • Edward Aboufadel
Reference work entry

Wavelets emerged in the late 1980s as a valuable new tool in science and engineering, and as a topic forfruitful mathematical research. Wavelet transforms are now regularly applied in areas such as image processing, statistical analysis, andseismic research. Wavelets are at the heart of the WSQ standard used by the United States' Federal Bureau of Investigation to compress fingerprint images [1]. They have been implemented in the Red professional digital video camera [2] and they are now being used in an attempt to analyzepaintings by famous artists [3]. In the past twenty years, related “-lets”tools have also emerged, such as ridgelets and shearlets (see  Curvelets and Ridgelets). The 1992 book by Daubechies [4] is a classic in the field.

Wavelet analysis shares with Fourier analysis the key idea of having a basis of functions with which to analyze signals and otherfunctions. While Fourier analysis uses sine and cosine functions (or complex exponentials) – which are smooth and...


Wavelet Analysis Wavelet Function Continuous Wavelet Transform Wavelet Filter Fingerprint Image 
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  1. 1.
    Bradley J, Brislawn C, Hopper T (1993) The FBI wavelet/scalar quantization standard for gray-scale fingerprint image compression. In: Proc Conf Visual Info Process II Proc SPIE, vol 1961. pp 293–304Google Scholar
  2. 2.
    RED Digital Cinema Camera Company
  3. 3.
    Lyu S, Rockmore D, Farid H (2004) A digital technique for art authentication. Proc Nat Acad Sci 101:17006–17010CrossRefGoogle Scholar
  4. 4.
    Daubechies I (1992) Ten lectures on wavelets. SIAMGoogle Scholar
  5. 5.
    Feng P et al (2007) Enhancing retinal image by the Contourlet transform. Pattern Recognit Lett 28:516–522CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Edward Aboufadel
    • 1
  1. 1.Department of MathematicsGrand Valley State UniversityAllendaleUSA