报告题目：Reconstruction of inhomogeneous media by an iteration algorithm with a learned projector

报 告 人：李凯

报告时间：2024年5月24日11:00-12:00

报告地点：格物楼数学研究中心528报告厅

报告摘要：In this talk, we mainly consider the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear), and certain regularization strategy is thus needed. However, it is difficult to select an appropriate regularization strategy which should enforce some a priori information of the unknown scatterer. To address this issue, we plan to use a deep learning approach to learn some a priori information of the unknown scatterer from certain ground truth data, which is then combined with a traditional iteration method to solve the inverse problem. Specifically, we propose a deep learning-based iterative reconstruction algorithm for the inverse problem, based on a repeated application of a deep neural network and the iteratively regularized Gauss-Newton method (IRGNM). Our deep neural network (also called the learned projector) mainly focuses on learning the a priori information of the shape of the unknown contrast with a normalization technique in the training processes and is trained to act like a projector which is helpful for projecting the solution into some feasible region. Extensive numerical experiments show that our reconstruction algorithm provides good reconstruction results even for the high contrast case and has a satisfactory generalization ability. This is a joint work with Prof. Bo Zhang and Prof. Haiwen Zhang.

报告人简介：李凯，本科就读于四川大学，现于中国科学院大学数学与系统科学研究院张波研究员名下攻读博士学位。