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長沙理工大學學術活動預告

報告承辦單位: 數學與統計學院

報告題目:  Imaging of buried obstacles in a two-layered medium with phaseless far-field data

報告內容:  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.

報告人姓名:   張海文

報告人所在單位: 中科院應用數學所

報告人職稱/職務及學術頭銜:  副研究員

報告時間:  2020年10月29日15:40－16:25

報告方式: 理科樓A-419

報告人簡介:  中國科學院應用數學所副研究員。研究方向為聲波與電磁波反散射問題。在 SIAM J. Appl. Math.、SIAM J. Imaging Sci.、SIAM J. Sci. Comput.、Inverse Problems 等學術期刊上發表和接收論文20余篇。曾主持完成中國博士后科學基金項目和國家自然科學基金青年項目。目前正在主持國家自然科學基金面上項目。