Reference object techniques for phaseless inverse scattering problems

报告人：张德悦
报告地点：数学与统计学院501室
报告时间：2018年11月24日星期六15:30-16:30
报告摘要：

This talk is concerned with the recent progresses on the phaseless inverse scattering problems with auxiliary reference objects. By incorporating an additional reference ball to the scattering system and using the superposition of different incident waves, we rigorously prove that the location and shape of the obstacle as well as its boundary condition or the refractive index can be uniquely determined by the modulus of acoustic far-field patterns. A reference ball based iterative method is also developed to numerically reconstruct the location and shape of a sound-soft obstacle from phaseless far-field data. For phaseless inverse acoustic source scattering problem, we first propose a phase retrieval formula based on the reference point sources, and then reconstruct the source function using the Fourier method. Several numerical examples will be provided to demonstrate the effectiveness and robustness of these methods.

主讲人简介：
张德悦，男，吉林大学数学学院教授、博士生导师，1998年毕业于吉林大学数学学院信息与计算科学专业，获学士学位，2004年毕业于吉林大学数学研究所计算数学专业，获理学博士学位。目前研究领域为数学物理反问题，主要方向为波动方程反散射问题的数值分析与计算。已在“Inverse Problems”、“Advances in Computational Mathematics”等期刊发表多篇SCI检索学术论文，其中一篇论文入选反问题领域国际著名期刊“Inverse Problems”的2017年度“亮点论文”（Editorial Highlights）。主持国家自然科学基金面上项目两项，参与国家自然科学基金项目三项。