Recent Progress on Applied and Computational Harmonic Analysis (13w2187)
Elena Braverman (University of Calgary)
Bin Han (University of Alberta)
Ozgur Yilmaz (University of British Columbia)
and especially for associated postdoctoral fellows and graduate students to report the most recent results and
It will concentrate on recent advances on
applied and computational harmonic analysis, in particular, on next generation novel efficient mathematical multiscale
representation methods and fast computational algorithms to meet the ever increasingly challenging tasks arising
from many areas of sciences and applications. More specifically, we shall focus on multiscale based methods
and redundant representations, consisting of the following three closely related and integrated parts:
1. Subdivision schemes and multiresolution structure with applications in applied mathematics, geometric data analysis, and visualization/simulation in computer graphics.
2. Riesz wavelets in numerical solutions to partial differential equations (PDEs) including Riesz wavelets in bounded domains with nonuniform meshes and adaptive wavelet multiscale methods for numerical solutions to PDEs.
3. Redundant representation in signal/image processing including development of $SigmaDelta$ schemes for analog-to-digital conversion and applications of directional wavelet frames in digital image/signal processing coupled with Bregman iteration algorithm and optimization techniques.