Introduction to Wavelets

  • Date: 07/18/2006

Ingrid Daubechies (Princeton University)


Simon Fraser University


Wavelets are a new approach 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, similar to zooming in with a camera. For this
reason, the wavelet transform is sometimes called a "mathematical microscope".

Wavelets are used by many scientists and engineers for a wide range of
applications. In particular, they have been incorporated in the JPEG2000
image compression standard.

The talk will start by explaining the basic principles of wavelets, which
are very simple. Then they will be illustrated with some examples,
including pictures of the wavelet scheme used by the FBI. Throughout
the talk we will see how wavelets emerged as a synthesis of ideas from
many different directions.


Ingrid Daubechies is currently the
William R. Kenan Jr. Professor
with the Mathematics Department
and the Program in Applied and
Computational Mathematics at
Princeton University. The work
of Prof. Daubechies has been fundamental
in the development of
the mathematics of time-frequency
analysis, in particular the
theory of wavelets. She has received numerous
awards including the Gold medal from the Flemish
Royal Academy of Arts and Sciences (Belgium), the
National Academy of Sciences (USA) Medal in
Mathematics, and the IEEE Information Theory Society
Golden Jubilee Award for Technological Innovation.
She is also the recipient of both the Ruth
Lyttle Satter and Steele Prizes from the American
Mathematical Society, the latter for her exposition
Ten Lectures on Wavelets. She was elected to the
National Academy of Sciences in 1998.

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