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Topological Derivative for Fast Imaging of Two-Dimensional Thin Dielectric Inclusions in The Wave Propagation Environment

  • Park, Won-Kwang (Department of Mathematics, The College of Natural Sciences, Kookmin University)
  • Received : 2010.11.26
  • Accepted : 2011.02.15
  • Published : 2011.03.31

Abstract

In this paper, we consider the topological derivative concept for developing a fast imaging algorithm of thin inclusions with dielectric contrast with respect to an embedding homogeneous domain with a smooth boundary. The topological derivative is evaluated by applying asymptotic expansion formulas in the presence of small, perfectly conducting cracks. Through the careful derivation, we can design a one-iteration imaging algorithm by solving an adjoint problem. Numerical experiments verify that this algorithm is fast, effective, and stable.

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Cited by

  1. Shape Reconstruction of Thin Electromagnetic Inclusions via Boundary Measurements: Level-Set Method Combined with the Topological Derivative vol.2013, 2013, https://doi.org/10.1155/2013/125909
  2. Improved subspace migration for imaging of small and arc-like perfectly conducting cracks vol.28, pp.4, 2014, https://doi.org/10.1080/09205071.2013.866526