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MULTISTATIC IMAGING OF EXTENDED TARGETS HABIB AMMARI, JOSSELIN GARNIER, HYEONBAE KANG, MIKYOUNG LIM, AND KNUT
 

Summary: MULTISTATIC IMAGING OF EXTENDED TARGETS
HABIB AMMARI, JOSSELIN GARNIER, HYEONBAE KANG§, MIKYOUNG LIM¶, AND KNUT
SØLNA
Abstract. In this paper we develop iterative approaches for imaging extended inclusions from multi-
static response measurements at single or multiple frequencies. Assuming measurement noise, we perform a
detailed stability and resolution analysis of the proposed algorithms in two different asymptotic regimes. We
consider both the Born approximation in the nonmagnetic case and a high-frequency regime in the general
case. Based on a high-frequency asymptotic analysis of the measurements, an algorithm for finding a good
initial guess for the illuminated part of the inclusion is provided and its optimality is shown. We illustrate
our main findings with a variety of numerical examples.
Key words. extended target, shape recovery, multi-static imaging, weighted subspace migration, sta-
bility and resolution analysis, optimal control
AMS subject classifications. 35R30, 35B30
1. Introduction. Recently, we have been interested in the problem of locating and es-
timating the geometric features of small inclusions (compared to the operating wavelength),
using arrays of point source transmitters and receivers at single or multiple frequencies.
This measurement configuration gives the so-called multistatic response matrix (MSR). In
[2], using long-wavelength asymptotic expansions of the measurements of high-order, we
have shown how the electromagnetic parameters and the equivalent ellipse of the target
can be reconstructed. We have also proposed an optimization approach to image geometric

  

Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique

 

Collections: Mathematics