Non-negativity preserving iterative regularization algorithms for ill-posed inverse problems

发布者:闻天明发布时间:2019-11-19浏览次数:10

Speak:     Prof. Ye Zhang

Time:       15:00-16:00, Nov. 21

Location:  SIST 1A-200

Host:       Prof. Yue Qiu

Abstract:

Many inverse problems are concerned with the estimation of non-negative parameters. In this talk, in order to obtain a stable non-negative approximate solution, we develop two novel non-negativity preserving iterative regularization methods. In contrast to the projected Landweber iteration, which has only weak convergence w.r.t. noise for the regularized solution, the newly introduced regularization methods exhibit the strong convergence. The convergence result for the imperfect forward model, as well as the convergence rates, are discussed. Two new discrepancy principles are developed for a posteriori stopping of our iterative regularization algorithms. As an application of our new approaches, we consider a biosensor problem, which is modelled as a two dimensional Fredholm integral equation of the first kind. Several numerical examples, as well as a comparison with the projected Landweber method, are given to show the accuracy and the acceleration effect of our new methods.

Bio:

Dr. Ye Zhang obtained the Ph.D in Mathematical Physics from Lomonosov Moscow State University in Russia in 2014. He received Chinese Government Award for Outstanding Self-Financed Students Abroad in 2012. From 2014 to 2017, he was a Postdoc and then a Senior Researcher at Örebro University and Karlstad University in Sweden. From 2018 to 2019, he held a Postdoctoral Fellowship of Alexander von Humboldt Foundation at the Chemnitz University of Technology in Germany. Since September 2019 he is an Associate Professor at Shenzhen MSU-BIT University in China. His main interest is Mathematical Theory and Numerical Methods of Ill-Posed Inverse Problems. He published more than 20 original papers in top journals such as Inverse Problems, Journal of the American Statistical Association, Fractional Calculus and Applied Analysis, etc.

Sist seminar 18220