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arXiv · 1706.04418

Reconstruction via the intrinsic geometric structures of interior transmission eigenfunctions

Jingzhi Li·Xiaofei Li·Hongyu Liu
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Abstract

We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties of the so-called interior transmission eigenfunctions, we develop a novel inverse scattering scheme. The proposed method can efficiently capture the cusp singularities of the support of the inhomogeneous medium. If further a priori information is available on the support of the medium, say, it is a convex polyhedron, then one can actually recover its shape. Both theoretical analysis and numerical experiments are provided. Our reconstruction method is new to the literature and opens up a new direction in the study of inverse scattering problems.

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Jingzhi Li, Xiaofei Li, Hongyu Liu. 2017-06-14. Reconstruction via the intrinsic geometric structures of interior transmission eigenfunctions. https://arxiv.org/abs/1706.04418

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