### Friday, October 31

## IP6

Second Generation Wavelets: Theory and Applications

1:30 PM-2:30 PM

*Chair: John G. Lewis, Boeing Information and Support Services, The Boeing Company*

*Room: Ballroom 3*

In the last decade wavelets have been applied successfully to sound (1D), image (2D), and video (3D) processing. Typical applications include compression, noise reduction, progressive transmission, etc. Each time the data is defined on an Euclidean space R^n and sampled on a regular grid.

Many applications, however, need wavelets defined on general geometries (curves, surfaces, manifolds), wavelets adjusted to irregular sampling, or adaptive wavelet transforms. Therefore we introduce Second Generation Wavelets: wavelets which are not necessarily translates and dilates of one function, but still enjoy all powerful properties such as time-frequency localization, multiresolution, and fast algorithms.

While the Fourier transform has been the principal tool in constructing classical wavelets, e.g. Daubechies, it can no longer be used to build Second Generation Wavelets. We present the lifting scheme, an entirely spatial construction technique for Second Generation Wavelets.

The speaker will give examples how lifting can be used to build wavelets for irregular samples, spherical wavelets, and multiresolution geometry. He will also show that all classical wavelets can be obtained through lifting, that lifting speeds up the fast wavelet transform by a factor of two, and that lifting allows for integer-to-integer wavelet transforms which are important in lossy compression. (ps: No preliminary knowledge of wavelets will be assumed).

**Wim Sweldens**

*Bell Laboratories, Lucent Technologies*

LA97 Homepage | Program Updates| Registration | Hotel Information | Transportation |
Program-at-a-Glance |

*MMD, 6/26/97*