Computational Algebraic Problems from Variational PDE Image Processing
by
Tony Chan
Department of MathematicsUniversity of California, Los Angeles
Box 951555, Los Angeles, CA 90095
Email: TonyC@college.ucla.edu
Abstract : Variational PDE models have
emerged over the last decade as very effective for image processing.
They posses desirable properties such as preserving edge sharpness,
good control of geometric features of objects, and a deep mathematical
foundation. At the same time, they also present significant
computational challenges as such models are highly nonlinear, possibly
locally singular/degenerate, in addition to the usual spatial stiffness
of PDE problems. In my talks, I'll review some of these issues, as well
as some approaches that have been proposed by us and others to deal
with them. The techniques include direct optimization algorithms,
primal-dual methods, and multigrid methods.
