Colloquium Announcement
Department of Mathematics
West Virginia University

for

Thursday, Mar 19, 1998, at 3:45pm in 324 Armstrong Hall

(Tea and cookies begin at 3:00 in coffee room.)

Professor Harvey Diamond

WVU


The Daubechies Orthonormal Wavelet Basis

The talk will be suitable for a general audience.

Students are strongly encouraged to participate.

Abstract



Many of you have heard the term "wavelets" and perhaps have wondered, "What's the buzz?". It began with the 1988 publication by Ingrid Daubechies of a method for constructing functions, called "wavelets", possessing some remarkable properties. Each wavelet could be used, through a discrete set of its translations and scalings, to represent any square-integrable function on the real line; wavelets could be constructed so as to possess any prespecified number of derivatives; they were each zero off of a finite interval; and all of the translations and scalings used in a given representation were orthogonal to each other! In short, just about everything you could ask for in a basis. Wavelet representations are especially good for approximating behavior at different scales, for removing high frequency noise, and for detecting features. In the talk we will go through the Daubechies construction in an informal fashion, introducing along the way some of the general ideas of discrete wavelet analysis, such as multiresolution analysis, recursively defined functions, and decomposition-reconstruction algorithms. To follow the development, one need only have minimal exposure to the language of vector spaces, orthogonal expansions, and Fourier series/transforms.
The information on the future (and past) Colloquia can be also found on web at the address:
http://www.math.wvu.edu/homepages/kcies/colloquium.html