# 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.

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.