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Asymptotic Property of Phaseless Total-Field Operators and Phaseless Inverse Scattering Problems

讲座摘要 

In this talk, we consider inverse scattering with phaseless total-field data at a fixed frequency. We will propose a new framework to study this problem, including the uniqueness issue and a factorization-type imaging algorithm. Precisely, we will establish the asymptotic property in an operator norm of the phaseless total-field operator defined in terms of the phaseless total-field data measured on a large enough ball, employing the theory of oscillatory integrals. As far as we know, this is the first result on the asymptotic behavior in an operator norm of the phaseless total-field operator though pointwise asymptotic results of the phased scattered field have been previously obtained. This asymptotic property of the phaseless total-field operators is then used to establish uniqueness results and an approximate factorization method for inverse scattering with phaseless total-field data at a fixed frequency. 


个人简介 
张波,1983 年毕业于山东大学数学系,1985 年在西安交通大学获硕士学位, 1992 年在英国 Strathclyde 大学获博士学位。现任中科院数学与系统科学研究院“百人计划”研究员,应用数学研究所副所长,反问题国际联合会东亚分会副主席,中国数学会常务理事,中国工业与应用数学学会常务理事、奖励工作委员会副主任、大数据与人工智能专委会副主任兼秘书长。在波传播与散射、反问题与成像、机器学习与智能数据分析的理论和算法方面均做出了重要贡献,在国际高水平学
术期刊发表论文130 余篇,得到了众多同行的引用和高度评价。