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.
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Aboufadel E et al. (2011) Wavelet-Kruskal solution to the InnoCentive Boston pothole challenge – software release. http://scholarworks.gvsu.edu/mathundergrad/1/
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 1961:293–304
Daubechies I (1992) Ten lectures on wavelets. SIAM, Philadelphia
Feng P et al (2007) Enhancing retinal image by the Contourlet transform. Pattern Recognit Lett 28:516–522
Lyu S, Rockmore D, Farid H (2004) A digital technique for art authentication. Proc Natl Acad Sci 101:17006–17010
RED Digital Cinema Camera Company. www.red.com
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Aboufadel, E. (2014). Wavelets, Introduction to. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-3-642-27737-5_587-3
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DOI: https://doi.org/10.1007/978-3-642-27737-5_587-3
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