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maintained by
Edward Aboufadel and Steven Schlicker
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| Discovering Wavelets: Student Work
maintained by
Edward Aboufadel and Steven Schlicker
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During the summer 2006 NSF-sponsored REU at GVSU, Tim Armstrong and Liz Smietana developed position codes. A position code is a matrix of symbols (often 0's and 1's, but other symbols can be used) so that by reading and processing a small submatrix of the code, the exact location in the matrix can be determined. The Anoto Pattern is a postion code that is used by the Fly Pentop Computer. One of the position code uses binary wavelets, while the other uses a base-12 idea.
A manuscript is available at the arXiv.
During the summer 2005 NSF-sponsored REU at GVSU, Beverly Lytle and Caroline Yang developed a wavelet-based method to tell whether or not a handwriting sample is genuine or an attempt at imitation.
An article about this work appeared in 2006 in the Rose Hulman Undergraduate Mathematics Journal.
During the summer 2004 NSF-sponsored REU at GVSU, Kevin Brink and Drew Colthorp developed filtered digitized aerial photographs with 2D wavelet filters, and then used the output of the filters to locate airplanes in photographs. Here are two examples:
Contact Prof. Edward Aboufadel for more information.
During the summer 2003 NSF-sponsored REU at GVSU, Julie Olsen and Jesse Windle developed wavelet-based methods to read characters from CAPTCHAs. Here is an example of a CAPTCHA:
An article about this work appeared in the March 2005 issue of the College Mathematics Journal.
Luis von Ahn, one of the inventors of CAPTCHAs, won a MacArthur Fellowship in 2006.
During the summer 2002 NSF-sponsored REU at GVSU, Lisa Driskell developed a method to embed messages in images using bivariate Haar wavelets. An article about this work appeared in the April 2004 issue of Cryptologia.
During the summer 2000 NSF-sponsored REU at GVSU, Amanda Cox and Amy Vander Zee worked with Edward Aboufadel on an undergraduate research project to classify all Daubechies scaling functions of two variables that reproduce constant and linear functions. A PDF pre-print is available.
This material is based upon work supported by the National Science Foundation under Grants No. DMS-0451254, DMS-0137264, and DMS-9820221. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).
An undergraduate wavelets course at Johns Hopkins University, which included projects.
An undergraduate wavelets course at the University of Saint Thomas, which included projects.
A Modified Hanning Wavelet, by three Romanian researchers (in physics and engineering), may be of interest to undergraduates.
These links will lead you to projects that used the book Discovering Wavelets as a resource.
Wavelet Analysis of a Beech 1900C Cockpit Voice Recorder.
Selective Image Compression of Passport Photographs using Wavelets and Neural Networks, by Hong Chung, Kwan-yu Lai, Alfred T. Lip, and Joe Yip
Image Compression Using Wavelets, by Karen Lees.
Wavelet Signal Processing of Digital Audio with Applications in Electro-Acoustic Music, by Corey Cheng at Dartmouth.
Computer Tomography, by
Rebecca Morganstern.
Local Computerized Tomography, by Lucia Wiguno.
Wavelet Based Image Compression, by a team of students at Rice University.