2017/06/14 by Jingzhi Li, Xiaofei Li, Li, Jingzhi +3 · 2 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.1706.04418
openalex publication_date 2017/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.