Speaker:
Prof. Guowei Wei ,
Michigan State University
Title:
PDE Transform --- A Unified Paradigm for Image Analysis and
Multiscale Modeling
Abstract:
The past two decades have witnessed increasing interest in geometric
partial differential equations (PDEs). However, much attention
is paid to the use of second-order geometric PDEs as low-pass
filters in signal, image and data analysis. My talk focuses on some
non-conventional aspects of geometric PDEs. First, I discuss
the construction of arbitrarily high-order geometric PDEs and their
utility for image and surface analysis. Additionally, the
design of nonlinear high-pass filters from a coupled PDE system is
illustrated. Appropriate combination of geometric PDEs gives rise to
the PDE transform. Like the wavelet transform, the PDE
transform is able to decompose signal, image and data into
functional modes with controllable time-frequency
localizations. The inverse PDE transform leads to a perfect
reconstruction. Finally, I analyze the geometric feature of
the PDE transform that offers a powerful means for the multiscale
modeling of biomolecular systems. The resulting differential
geometry based multiscale models encompass discrete atomistic
descriptions of macromolecules and continuum macroscopic
descriptions of solvent. Applications are discussed to biomedical
images, molecular solvation, virus surface formation,
protein-protein interactions, multiscale molecular dynamics, and ion
channel transport.