主题：Introduction of inverse problems
内容简介：Inverse problems play a critical role in many application areas, where one wishes "invert" a set of measurements/data to reconstruction an approximation of the physical properties. Medical imaging is perhaps the most well-known example, while others include nanoscale electron/neutron tomography, seismic imaging, and helioseismology. In this talk, I will give an introduction to some of the fundamental concepts involved in inverse problems, including some examples, ill/well-posedness, regularization techniques, variational methods. The talk starts with some motivating examples of Inverse Problems before introducing the general setting. Then, I will explain why inverse problems are difficult to solve, and simply introduce the basic idea behind regularization technique. In the end, I will give a short introduction on variational methods, which play an important role in inverse problems.
This talk is not to bring you to the frontier of the research field on inverse problems, but to give you an overview of this field.
Yiqiu Dong is an associate professor in Department of Applied Mathematics and Computer Science of Technical University of Denmark. She is mainly working on the ERC-project "High-Definition Tomography".
She received her Ph.D. degree in Computational Mathematics from Peking University in 2007 under the supervision of Prof. Shufang Xu (Peking University) and Prof. Raymond Honfu Chan (The Chinese University of Hong Kong, joint Ph.D. program). After that, she moved to Austria, and was a postdoctoral researcher in Institute of Mathematics and Scientific Computing at the Karl-Franzens University of Graz. She worked in the SFB-project "Mathematical Optimization and Applications in Biomedical Sciences" with Prof. Michael Hintermüller. In 2010, she got the scientific researcher position in Institute of Biomathematics and Biometry of Helmholtz Zentrum Muenchen, which is the German research center for environmental health.
Her research areas include mathematical imaging, inverse problem and variational methods, matrix application and computation, and optimization methods.