DIRECT SAMPLING METHODS FOR ISOTROPIC AND ANISOTROPIC SCATTERERS WITH POINT SOURCE MEASUREMENTS

Isaac Harris, Dinh Liem Nguyen, Thi Phong Nguyen

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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 iden-tities. Numerical experiments are given in two dimensions for both isotropic and anisotropic scatterers.

Original languageEnglish (US)
Pages (from-to)1137-1162
Number of pages26
JournalInverse Problems and Imaging
Volume16
Issue number5
DOIs
StatePublished - Oct 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

Keywords

  • Inverse scattering
  • direct sampling method
  • factorization method
  • isotropic and anisotropic scatterers
  • near-field data

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