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Journal of Applied Nonlinear Dynamics 1(3) (2012) 227--237 | DOI:10.5890/JAND.2012.07.001

Keehwan Kim $^{1}$ , Koung Hee Leem $^{2}$, George Pelekanos $^{2}$

$^{1}$ Department of Mathematics, Yeungnam University, 719-749, Gyeongsangbuk-do, South Korea

$^{2}$ Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, IL 62026, USA

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Abstract

In this paper, we propose a new and efficient regularization technique (Singular Perturbation Technique-SPT) for the reconstruction of the shape of a scatterer from far field measurements. The approach used is based on the linear sampling method and uses singular perturbations of the identity along with Neumann series approximations to recover the shape of the unknown object. In comparison with the well established Tikhonov-Morozov regularization techniques our new algorithm appears to be more computationally efficient as it doesn’t require computation of the regularization parameter for each point in the grid. Moreover reconstructions obtained using (SPT) compare well with those obtained using other existing regularization methods.

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