Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Wavelets, Introduction to

  • Edward Aboufadel
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_587-3

Wavelets emerged in the late 1980s as a valuable new tool in science and engineering and as a topic for fruitful mathematical research. Wavelet transforms are now regularly applied in areas such as image processing, statistical analysis, and seismic research. Wavelets are at the heart of the WSQ standard used by the United States Federal Bureau of Investigation to compress fingerprint images (Bradley et al. 1993). They have been implemented in the Red professional digital video camera (Red Digital Cinema Camera Company) and in an analysis of paintings by famous artists (Lyu et al. 2004). A wavelet-based algorithm was accepted by the city of Boston as one of the winners of a contest to detect potholes using smartphone sensors (Aboufadel et al. 2011). 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 (Daubechies 1992) is a classic in the field.

Wavelet analysis shares with...


Wavelet Analysis Wavelet Transformation Scaling Function Wavelet Function Mother Wavelet 
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  1. Aboufadel E et al. (2011) Wavelet-Kruskal solution to the InnoCentive Boston pothole challenge – software release. http://scholarworks.gvsu.edu/mathundergrad/1/
  2. Bradley J, Brislawn C, Hopper T (1993) The FBI wavelet/scalar quantization standard for gray-scale fingerprint image compression. Proc Conf Vis Info Process II Proc SPIE 1961:293–304ADSGoogle Scholar
  3. Daubechies I (1992) Ten lectures on wavelets. SIAM, PhiladelphiaCrossRefzbMATHGoogle Scholar
  4. Feng P et al (2007) Enhancing retinal image by the Contourlet transform. Pattern Recognit Lett 28:516–522CrossRefGoogle Scholar
  5. Lyu S, Rockmore D, Farid H (2004) A digital technique for art authentication. Proc Natl Acad Sci 101:17006–17010ADSCrossRefGoogle Scholar
  6. RED Digital Cinema Camera Company. www.red.com

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsGrand Valley State UniversityAllendaleUSA