2021/07/16 by Isaac Harris, Harris, Isaac, Dinh-Liem Nguyen +3 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.2107.08138
openalex publication_date 2021/07/16 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper, we consider the inverse scattering problem for recovering either an isotropic or anisotropic scatterer from the measured scattered field initiated by a point source. We propose two new imaging functionals for solving the inverse problem. The first one employs a far-field transform to the data which we then use to derive and provide an explicit decay rate for the imaging functional. In order to analyze the behavior of this imaging functional we use the factorization of the near field operator as well as the Funk-Hecke integral identity. For the second imaging functional the Cauchy data is used to define the functional and its behavior is analyzed using the Green's identities. Numerical experiments are given in two dimensions for both isotropic and anisotropic scatterers.