HISTORY – PROBLEM – DECISION – WSQ – NCHANNELS

ZEROTREE – CONCLUSION – REFERENCES

The subject of wavelets has become an increasingly popular topic of study in recent years. The number of applications of wavelets is countless in the fields of mathematics, quantum physics, electrical and nuclear engineering, geology, astronomy, and even finance. Many new wavelet applications have recently been developed while interchanging these fields. Some interesting examples of real life wavelet applications include image compression, earthquake prediction, musical restoration, turbulence, speech discrimination, and human vision. The content of this paper will explore how the Federal Bureau of Investigation (FBI) uses wavelets in their fingerprint files to compress, transmit, and store images of millions of fingerprints. Wavelets are used in areas such as this to process and compress large amounts of data.

The basic idea of wavelets is to analyze with respect to scale. A wavelet is a type of mathematical function that divides up specific data into components of different frequencies, and then analyzes each component with a specific resolution according to the scale of the frequency. In much the same way as Riemann Sums are used to approximate an area under a curve, wavelets can be used to approximate different types of functions, and the more iterations or steps used in the calculation, the better the resolution becomes.

Because of their ability to greatly compress large images or signals, wavelets can be used to represent other functions, especially functions that are much to large and difficult to work with. Compression using wavelets is often lossy, which means that compression cannot be reversed and all the original data may not be reproduced. However, the lost data is often very small or insignificant in relation to the signal as a whole. To minimize lost data and to better approximate a signal, different so-called “families” of wavelets can be used. The Haar wavelets and the Daubechies wavelets are the most common wavelet families. The different types of wavelet families allows the user to select which set of wavelets would be the best and most appropriate for a specific application.

* Kalyn Gzym and Todd Frazee designed this web page for a semester project in Fall 2001. It is based on the report they wrote while attending Grand Valley State University, Allendale, MI – USA. Any information that may be of help to you in study and research is encouraged.