Campuses:

Math matters public lecture: Surfing with wavelets

Wednesday, October 29, 2008 - 8:00pm - 9:15pm
Willey Hall 125
Ingrid Daubechies (Princeton University)
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.