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.
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