Abstract
In this paper, we consider the recently developed level set evolution technique in order to reconstruct two-dimensional thin electromagnetic inclusions with dielectric or magnetic contrast with respect to the embedding homogeneous medium. For a successful reconstruction, two level set functions are employed; the first one describes the location and shape, and the other one the connectivity and length. Speeds of evolution of level set functions are calculated via Fréchet derivatives by means of an adjoint technique. Several numerical experiments illustrate how the proposed method behaves.
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References
Àlvarez, D., Dorn, O., Moscoso, M.: Reconstructing thin shapes from boundary electrical measurements with level sets. Int. J. Inf. Syst. Sci 2, 498–511 (2006)
Ammari, H.: An Introduction to Mathematics of Emerging Biomedical Imaging. Mathematics and Applications Series. Mathematics and Applications Series, vol. 62. Springer, Berlin (2009)
Ammari, H., Beretta, E., Francini, E.: Reconstruction of thin conductivity imperfections. Applicable Analysis 83, 63–76 (2004)
Ammari, H., Beretta, E., Francini, E.: Reconstruction of thin conductivity imperfections, II. The case of multiple segments. Applicable Analysis 85, 87–105 (2006)
Dorn, O., Lesselier, D.: Level set methods for inverse scattering. Inverse Problems 22, R67–R131 (2006)
Lee, H., Park, W.K.: Location search algorithm of thin conductivity inclusions via boundary measurements. In: ESAIM: proc., vol. 26, pp. 217–229 (2009)
Osher, S., Fedkiw, R.: Level set methods and dynamic implicit surfaces. Springer, New York (2003)
Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)
Park, W.K.: Inverse scattering from two-dimensional thin inclusions and cracks. Thèse dedoctorat, Ecole Polytechnique (available via ParisTech) (2009), http://paristech.bib.rilk.com/4834
Park, W.K., Ammari, H., Lesselier, D.: On the imaging of two-dimensional thin inclusions by a MUSIC-type algorithm from boundary measurements. Electromagnetic Nondestructive Evaluation (XII), Studies in Applied Electromagnetics and Mechanics 32, 297–304 (2009)
Park, W.K., Lesselier, D.: MUSIC-type imaging of a thin penetrable inclusion from its multi-static response matrix. Inverse Problems 25, 075002 (2009)
Park, W.K., Lesselier, D.: Reconstruction of thin electromagnetic inclusions by a level set method. Inverse Problems 25, 085010 (2009)
Ramananjaona, C., Lambert, M., Lesselier, D., Zolésio, J.-P.: Shape reconstruction of buried obstacles by controlled evolution of a level set: from a min-max formulation to numerical experimentation. Inverse Problems 17, 1087–1111 (2001)
Santosa, F.: A level set approach for inverse problems involving obstacles. ESAIM Control Optim. Calc. Var. 1, 17–33 (1996)
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Park, WK., Lesselier, D. (2010). Level Set Method for Reconstruction of Thin Electromagnetic Inclusions. In: Lee, J.H., Lee, H., Kim, JS. (eds) EKC 2009 Proceedings of the EU-Korea Conference on Science and Technology. Springer Proceedings in Physics, vol 135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13624-5_11
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DOI: https://doi.org/10.1007/978-3-642-13624-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13623-8
Online ISBN: 978-3-642-13624-5
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