Uniqueness, Reconstruction Algorithms and Invisibility Cloaking for Inverse Scattering Problems

  • LIU, Hongyu (PI)

Project: Research project

Project Details


This project proposes to continue the PI's research on uniqueness, numerical reconstruction algorithms and invisibility cloaking for inverse acoustic and electromagnetic (EM) scattering problems. Inverse scattering problems concern the recovery of unknown/inaccessible objects by acoustic or electromagnetic wave measurements. They are of central importance to many areas of science and technology, including radar and sonar, geophysical exploration, medical imaging, non-destructive testing and remote sensing. However, there are various challenging problems in this field that are far from well understood. Our proposed studies lie in the core of research on inverse scattering problems.

For uniqueness, we propose to establish the unique determination of an isotropic acoustic/EM medium by the fixed-incident-direction far-field data. The inverse problems are formally posed with such measurement data. To our best knowledge, there is no such uniqueness result in the literature. The study is based on showing the discreteness of certain acoustic and electromagnetic interior transmission eigenvalues with generic mediums. The uniqueness result would motivate some new inverse scattering modalities.

For the numerical reconstruction algorithm, we propose to investigate a novel multiple- shot method, extending the single-shot method developed by the PI and his collaborators in their recent works for inverse scattering problems. The single-shot method makes use of a single far-field measurement, whereas the multiple-shot method would make use of multiple far-field measurements. The extension is highly non-trivial and the proposed method could produce fine reconstructions for some important inverse scattering problems. Particularly, we shall apply the newly developed method to the reconstruction of buried anomalies in a two-layered medium, and to the ground detection with non- flat/rough background ground.

Finally, we consider the approximate invisibility cloaking for acoustic and electromagnetic waves. The transformation-optics invisibility cloaking has been widely investigated in the literature in recent years. However, the cloaking mediums obtained via the transformation-optics approach are usually anisotropic. The anisotropy causes sever difficulties for practical realization of the cloaking devices. We shall develop a general framework of constructing isotropic cloaking devices. The major idea is to investigate the so-called non-scattering potential.
Effective start/end date1/09/1531/08/18


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