ABSTRACT

The goal of this talk is to show you a gallery of my recent works focusing on inverse problems with various applications ranging from image processing, computer graphics, and dynamic identification from data. Specifically, for image processing, we will talk about the lattice metric space proposed for quantifying visual differences among lattice patterns, color recovery for underwater images, variational surface from point cloud, and a deep learning based low-rank reconstruction for medical image sequences; for computer graphics, we will discuss a novel image vectorization technique based on affine shortening flow and its extension to color images; for dynamic identification, we shall present some newly proposed effective and robust algorithms and more importantly, some theoretical results. For each topic, I will present representative works, show their key ideas, and illustrate the methods' performances and implications via numerical experiments and comparison studies