## 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.

**Bio:**

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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