Computational Algebraic Problems from Variational PDE Image Processing


Tony Chan

Department of Mathematics
University of California, Los Angeles
Box 951555, Los Angeles, CA 90095

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.

Lecture Slide