报告题目：Accelerated regularization methods for linear inverse problems, with application to bioluminescence tomography
报告人：龚荣芳副教授，南京航空航天大学
报告时间：2020年11月1日上午10:00-12:00
报告地点：数理楼135报告厅
摘要：In this talk we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a linear vanishing damping term, which can be viewed not only as a extension of the asymptotical regularization, but also as a continuous analog of the Nesterov's acceleration scheme. New iterative regularization methods are derived from this continuous method in combination with damped symplectic numerical schemes. The regularization property as well as convergence rates and acceleration affects under the Holder-type source conditions of both continuous and discretized methods are proven. The second part of this talk is concerned with the application of the newly developed accelerated iterative regularization methods with a posteriori stopping rule to the diffusion based bioluminescence tomography. Several numerical examples are given to show the accuracy and the acceleration effect of the new method.
报告人简介: 龚荣芳，南京航空航天大学数学系副教授。2009年浙江大学博士毕业后进入南京航空航天大学数学系工作。期间于2014年5月至2015年5月在美国Iowa大学数学系，2016年7月至9月在瑞典Orebro大学数学系，2018年7月至10月在澳大利亚国立大学数学系访问。龚荣芳博士主要研究医学成像、反传导率等应用反问题的正则化理论与方法。已发表SCI论文20多篇，他的研究成果发表于Numerische Mathematik, Inverse Problems, Inverse Problems and Imaging, Computational Methods in Applied Mechanics and Engineering等计算和应用数学的主流刊物上。主持完成国家青年基金、国家博士后基金、江苏省青年基金和江苏省博士后基金各1项，中央高校基础研究基金3项。目前主持国家自然科学基金面上项目1项，参与国家面上项目1项。