Research Seminar in Mathematics - Nonlinear Flows for Displacement Correction and Applications

Speaker

Dr. Guozhi Dong (University of Vienna, Austria)

Abstract

Partial differential equations (PDEs) are tightly connected to variational methods and energy optimization problems. In this talk we introduce some novel nonlinear evolution PDEs for correcting displacement errors in image data. The PDEs are derived from a family of non-convex regularization functionals which is behind an optimization model. Numerically, we show a convergence result and also the behavior of the flows. Some applications like dejittering image data and fixing angular uncertainty in tomography have been highlighted.

If time available, I can talk about a recent work on gradient recovery in manifold setting.

Title

Parametric polynomial preserving recovery on manifolds

Abstract

Gradient recovery is an important technique for post-processing numerical solutions and pre-processing image data. In this talk, I will present a recent work on gradient recovery in a manifold setting. It is a generalization of polynomial preserving recovery method which is introduced for planar problems. The new method has two significant improvements in comparing with methods in the state of the art: first, it does not ask for exact tangent spaces of the manifold, and second, it removes the O(h^2)-symmetric conditions from the existing methods for the super-convergence. I will mainly show the algorithms and numerical results.