报告题目： Tikhonov-type for inverse problems with multiple repeated measurement data in Banach spaces

  报告摘要：

We consider Tikhonov-type regularization for solving nonlinear inverse problems under the statistical framework that multiple unbiased independent identically distributed measurement data are available. We use the average of these data to reconstruct a solution whose feature is captured by a convex penalty term. Assuming certain conditions concerning the nonlinear operator, we derive the convergence rates where the regularization parameter can be chosen either a priori or a posteriori by the statistical sequential discrepancy principle. We further investigate the convexity of Tikhonov-type functionals and show the influence of the number of measurement data on it. We propose two globally convergent algorithms: the TIGRA-$\R$ algorithm for repeated measurements and the Dynamic TIGRA-R algorithm for sequential data. Finally, some numerical experiments illustrate the theoretic analysis and verify the effectiveness of the methods.

  报告时间：8月4日16：00-18：00，地点理学楼609

  专家简介：王薇，理学博士，嘉兴大学教授，硕士生导师。2011年4月在6163银河线路检测中心获得理学博士学位。2011年7月至2013年7月在复旦大学从事博士后研究工作。研究方向为反问题理论与计算，也包括地震波全波形反演、EIT问题、CT不完全数据的图像重构等应用。主持国家自然科学基金项目2项（青年基金项目、面上项目），浙江省自然科学基金项目2项（青年基金、一般项目），在Numer Math、Inverse Problems等有影响力的国际学术期刊上发表SCI论文30余篇。