Recovering a polyhedral obstacle by a few backscattering measurements

Jingzhi Li, Hongyu LIU*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

We propose an inverse scattering scheme of recovering a polyhedral obstacle in Rn, n= 2, 3, by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the modulus of the far-field pattern in the backscattering aperture possesses a certain local maximum behavior, from which one can determine the exterior normal directions of the front sides/faces. Then by using the phaseless backscattering data corresponding to a few incident plane waves with suitably chosen incident directions, one can determine the exterior unit normal vector of each side/face of the obstacle. After the determination of the exterior unit normals, the recovery is reduced to a finite-dimensional problem of determining a location point of the obstacle and the distance of each side/face away from the location point. For the latter reconstruction, we need to make use of the far-field data with phases. Numerical experiments are also presented to illustrate the effectiveness of the proposed scheme.

Original languageEnglish
Pages (from-to)2101-2120
Number of pages20
JournalJournal of Differential Equations
Volume259
Issue number5
DOIs
Publication statusPublished - 5 Sep 2015

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • Backscattering
  • Inverse scattering
  • Phaseless
  • Polyhedral obstacle

Fingerprint

Dive into the research topics of 'Recovering a polyhedral obstacle by a few backscattering measurements'. Together they form a unique fingerprint.

Cite this