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Discovering Wavelets: Wavelets and Image Compression Project
maintained by Edward Aboufadel and Steven Schlicker
Wavelets can be used to incorporate real applications into an upper-level mathematics course, namely Linear Algebra. The project described here is based on the idea of image compression. To motivate the need for compression of images we consider the problem faced by the FBI. The FBI fingerprint files contain over 25 million cards, each of which contains 10 rolled fingerprint impressions. Each card produces about 10 megabytes of data. To store all of these cards would require some 250 terabytes of space. Needless to say, without some sort of image compression, a sortable and searchable electronic database would be next to impossible. To deal with this problem, the FBI has adopted standards for fingerprint digitization using a wavelet compression standard The FBI Fingerprint Image Compression Standard. The project described here is influenced by ideas of Gilbert Strang. The Haar wavelets are represented as vectors in n-dimensional space and processing of data with Haar wavelets is accomplished through matrix operations.

This link is to the complete project, available as a pdf file. To view this document, you need the free Adobe Acrobat Reader. Go to the software page for the Pixel Images program, along with Maple files.