Wavelet Frames and
Applications
Zuowei Shen,
National University of Singapore
Abstract:
One of the major driving forces in the area of applied and computational
harmonic analysis during
the last two decades is the development and the analysis of redundant systems
that produce sparse
approximations for classes of functions of interest. Such redundant systems
include wavelet
frames, ridgelets, curvelets
and shearlets, to name a few. This talk focuses
on tight wavelet
frames that are derived from multiresolution analysis
and their applications in imaging.
The pillar of this theory is the unitary extension principle and its various generalizations,
hence we will first give a brief survey on the development of extension
principles.
The extension principles allow for systematic constructions of
wavelet frames that can be
tailored to, and effectively used in, various problems in imaging science. We
will discuss some of
these applications of wavelet frames. The discussion will include
frame-based image analysis and
restorations, image inpainting, image denosing, image deblurring and
blind deblurring, image
decomposition, and image segmentation.