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August  2009, 3(3): 389-403. doi: 10.3934/ipi.2009.3.389

Reciprocity gap music imaging for an inverse scattering problem in two-layered media

Roland Griesmaier 1,

1. 

Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, United States

Received  March 2009 Revised  May 2009 Published  July 2009

In this work we consider a modified MUSIC method for determining the positions of a collection of small perfectly conducting buried objects from measurements of time-harmonic electromagnetic fields on the surface of ground. This method is based on an asymptotic analysis of certain integrals of electric and magnetic fields, so-called reciprocity gap functionals, as the buried objects shrink to points. Unlike standard MUSIC reconstruction methods our algorithm avoids the computation of the Green's function for the background medium during the reconstruction process, but on the other hand it requires more measurement data. After describing the theoretical foundation of this reconstruction method, we provide numerical results showing its performance. We also compare these results to reconstructions obtained by a standard MUSIC algorithm.
Keywords: Maxwell's equations, layered media, asymptotic expansions., small scatterers, Inverse scattering, reciprocity gap functional.
Mathematics Subject Classification: Primary: 78A46, 35R30; Secondary: 35Q60, 35C2.
Citation: Roland Griesmaier. Reciprocity gap music imaging for an inverse scattering problem in two-layered media. Inverse Problems & Imaging, 2009, 3 (3) : 389-403. doi: 10.3934/ipi.2009.3.389
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