|Variational Partial Differential Equations and Sparse Representation|
|Time：||Mon/Tue 10:10-12:00, 08-05~09-03|
|Instructor：||Ye Duan [University of Missouri - Columbia]|
|Place：||Conference Room 3, Floor 2, Jin Chun Yuan West Building|
Variational Partial Differential Equations (PDEs) are emerging techniques for representing, deforming, and recovering structures in an arbitrary dimension across different fields (such as mathematics, fluid dynamics, graphics, imaging, and vision). Advances in numerical analysis have led to computationally efficient tools for computing and analyzing interface motion within variational PDEs frameworks in a host of application settings. Meanwhile, researchers have made significant progress in the past few years in using Sparse Representation: a linear combination of relatively few base elements in an over-complete dictionary, for acquiring, representing and compressing high-dimensional signals. In order to efficiently compute such sparse representations with high accuracy, various kinds of effective algorithms such as convex optimization, split Bregman, and greedy pursuit, etc have been proposed. This course will introduce students to both the theoretical foundations of Variational PDEs and Sparse Representation as well as the state-of-the-art in applying these techniques in areas such as medical imaging, computer animation, computer graphics, computer vision and virtual reality, etc. We will explore current research issues and will cover in depth the associated computational and numerical techniques. This course should be appropriate for graduate students in all areas as well as advanced undergraduate students.