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报告承办单位: 数学与统计学院

报告题目:  Imaging of buried obstacles in a two-layered medium with phaseless far-field data

报告内容:  This talk is concerned with the inverse problem of reconstructing the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. Similarly to the homogenous background medium case, for this problem it is also true that the modulus of the far-field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, and thus it is impossible to determine the location of the obstacle from such phaseless far-field data. Based on the idea of using superpositions of two plane waves with different directions as the incident fields, a direct imaging algorithm is developed to locate the position of small anomalies with the intensity of the far-field pattern measured in the upper half-space. This is a nontrivial extension of our previous work [Inverse Problems 34 (2018), 104005] from the homogenous background medium case to the two-layered background medium case. Both the limited aperture measurement data and the presence of the two-layered background medium lead to difficulties in the theoretical analysis of the proposed imaging algorithm. To overcome the difficulties we employ the theory of oscillatory integrals. Further, with the aid of the imaging algorithm, a recursive Newton-type iteration algorithm in frequencies is proposed to reconstruct both the location and shape of extended obstacles. Finally, numerical experiments are presented to illustrate the feasibility of our algorithms.

报告人姓名:   张海文

报告人所在单位: 中科院应用数学所

报告人职称/职务及学术头衔:  副研究员

报告时间:  2020年10月29日15:40－16:25

报告方式: 理科楼A-419

报告人简介:  中国科学院应用数学所副研究员。研究方向为声波与电磁波反散射问题。在 SIAM J. Appl. Math.、SIAM J. Imaging Sci.、SIAM J. Sci. Comput.、Inverse Problems 等学术期刊上发表和接收论文20余篇。曾主持完成中国博士后科学基金项目和国家自然科学基金青年项目。目前正在主持国家自然科学基金面上项目。