12:30pm
EQuad E415
Title:
Redundant Wavelet Frame Systems From Refinable Functions
Abstract:
Wavelet frames and dual/tight wavelet frames are redundant wavelet systems
which preserve many desirable properties of their corresponding well-known
non-redundant wavelet systems: Riesz wavelet bases and (bi)orthogonal wavelet
bases. In general, wavelet bases are derived from specific refinable
functions by multiresulition analyses. However, not every refinable function
can be used to derive a non-redundant wavelet system and the concrete procedure
to design such systems is far from straightforward and painless.
In this talk, we shall demonstrate that things are much easier for redundant
wavelet systems. We shall first give an example to illustrate that the
canonical dual frame of a wavelet frame may not have the desirable wavelet
structure, while the wavelet frame can still have dual frames with wavelet
structure. Then we shall discuss how to derive dual/tight wavelet frames
from any refinable functions. We shall demonstrate that for any refinable
function, a family of wavelet frames with explicit and simple expressions
can be easily derived and such wavelet frames can have any preassigned order
of vanishing moments. Examples of wavelet frames and dual/tight wavelet
frames derived from the B-spline functions will be presented to illustrate
the general theory.
This is joint work with Ingrid Daubechies, Amos Ron and Zuowei Shen.
http://www.math.princeton.edu/~bhan/research.html