Course Overview
Welcome to the Wavelets Webpage at the University of St. Thomas. Two National Science Foundation (DUE0442684 and DUE0717662) grants have supported the development of an undergraduate course on wavelets and their applications, two texts, software, final projects, and the Wavelets in Undergraduate Website. The course has been taught twelve times at the University of St. Thomas and world wide. prerequisite knowledge is the calculus sequence and familiarity with matrix arithmetic. The course makes heavy use of Mathematica (or MATLAB) and follows an applications- first model: Students are introduced to some rudimentary wavelet transforms, quantization tools, and coding schemes and then are immediately immersed in applications such as image compression and image boundary detection. The applications provide strong motivation to learn the more advanced mathematics necessary to build better image processing tools. Other
applications introduced along the way are audio de-noising and image segmentation. The course concludes with final projects where students can learn about new applications or delve deeper into some of the more theoretical aspects of the topic.
New Book!
New as of April 8, 2019 is the second edition of the book
Discrete Wavelet Transformations: An Elementary Approach with Applications, 2nd edition. The new book is a significant rewrite of the first edition. The book is divided into two parts - the first develops basic orthogonal and biorthogonal wavelet filters and transformations without the use of Fourier methods. The second portion of the book follows a more traditional development of filters using Fourier methods. New applications include image segmentation, image pan-sharpening and the FBI Fingerprint Compression Specification. Also included are new chapters on wavelet packets and lifting.
Previous Books
I have written a text,
Discrete Wavelet Transformations: An Elementary Approach with Applications, published on January 8, 2008, for an introductory course on discrete wavelets and applications.
A second book,
Wavelet Theory: An Elementary Approach with Applications, co-authored with
David Ruch, was published on October 26, 2009. This book is intended for use as a text in a topics course for advanced undergraduate or graduate students, or as a reference for professionals interested in an introduction to the elementary theory of wavelets.
You can view the table of contents, read an overview, learn about the intended audience, and see who is using the texts by clicking the appropriate link on the right menu.
Resources
The WaveletWare Package is available in Mathematica and MATLAB (coming soon). This add-on allows students or researchers to further explore discrete wavelet transformations and their applications. Also available under Resources at right are live examples and labs for use with a discrete wavelets course. The live examples allow users to reproduce many of the example results found in the new text and in many instances, offers questions or tasks that allow the user to further investigate or master a concept.