Recovering a polyhedral obstacle by a few backscattering measurements

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Original languageEnglish
Pages (from-to)2101-2120
Journal / PublicationJournal of Differential Equations
Issue number5
Online published8 Apr 2015
Publication statusPublished - 5 Sep 2015
Externally publishedYes


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.

Research Area(s)

  • Inverse scattering, Polyhedral obstacle, Backscattering, Phaseless

Citation Format(s)