Reciprocity gap music imaging for an inverse scattering problem in two-layered media
Roland Griesmaier
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
A note on analyticity properties of far field patterns
Roland Griesmaier Nuutti Hyvönen Otto Seiskari
In scattering theory the far field pattern describes the directional dependence of a time-harmonic wave scattered by an obstacle or inhomogeneous medium, when observed sufficiently far away from these objects. Considering plane wave excitations, the far field pattern can be written as a function of two variables, namely the direction of propagation of the incident plane wave and the observation direction, and it is well-known to be separately real analytic with respect to each of them. We show that the far field pattern is in fact a jointly real analytic function of these two variables.
keywords: partial data. Far field pattern inverse scattering analytic functions

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