University of Minnesota
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IMA Math Matters Lecture:

Surfing with Wavelets

Ingrid Daubechies
Department of Mathematics
and
Program in Applied and Computational Mathematics
Princeton University

October 29, 2008

7:00 pm, Willey Hall 125    Map

Lecture Video (flv)     Photo Gallery
Postcard:  pdf     University of Minnesota Press Release

Abstract:

Wavelets are used in the analysis of sounds and images, as well as in many other applications. The wavelet transform provides a mathematical analog to a music score: just as the score tells a musician which notes to play when, the wavelet analysis of a sound takes things apart into elementary units with a well defined frequency (which note?) and at a well defined time (when?). For images wavelets allow you to first describe the coarse features with a broad brush, and then later to fill in details. This is similar to zooming in with a camera: first you can see that the scene is one of shrubs in a garden, then you concentrate on one shrub and see that it bears berries, then, by zooming in on one branch, you find that this is a raspberry bush. Because wavelets allow you to do a similar thing in more mathematical terms, the wavelet transform is sometimes called a "mathematical microscope."

Wavelets are used by many scientists for many different applications. Outside science as well, wavelets are finding their uses: wavelet transforms are an intergral part of the image compression standard JPEG2000.

The talk will start by explaining the basic principles of wavelets, which are very simple. Then they will be illustrated with some examples, including an explanation of image compression.



Math Matters lectures feature distinguished mathematicians and scientists who are also superb expositors able to illuminate the role mathematics is playing in understanding our world and shaping our lives. The lectures are aimed at a broad audience.

 

Math Matters - Public Lecture Series