Imaging schemes for perfectly conducting cracks. (English) Zbl 1259.78049

Summary: We consider the problem of locating perfectly conducting cracks and estimating their geometric features from multistatic response matrix measurements at a single or multiple frequencies. A main objective is to design specific crack detection rules and to analyze their receiver operating characteristics and the associated signal-to-noise ratios. In this paper, we introduce an analytic framework that uses asymptotic expansions which are uniform with respect to the wavelength-to-crack size ratio in combination with a hypothesis test based formulation to construct specific procedures for detection of perfectly conducting cracks. A central ingredient in our approach is the use of random matrix theory to characterize the signal space associated with the multistatic response matrix measurements. We present numerical experiments to illustrate some of our main findings.


78M35 Asymptotic analysis in optics and electromagnetic theory
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
15B52 Random matrices (algebraic aspects)
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