East Asian mathematical journal

  • 제32권1호
  • /
  • Pages.129-138
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  • 2016
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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THE METHOD OF REGULARIZATION RATIOS APPLIED TO RECONSTRUCTIONS OF ELASTIC RIGID OBSTACLES VIA THE FACTORIZATION METHOD

  • Kim, K. (Department of Mathematics, Yeungnam University) ;
  • Leem, K.H. (Department of Mathematics and Statistics, Southern Illinois University) ;
  • Pelekanos, G. (Department of Mathematics and Statistics, Southern Illinois University)
  • 투고 : 2016.01.18
  • 심사 : 2016.01.30
  • 발행 : 2016.01.30
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초록

In this paper, we propose an efficient regularization technique (The Method of Regularized Ratios) for the reconstruction of the shape of a rigid elastic scatterer from far field measurements. The approach used is based on the factorization method and creates via Picard's condition ratios, baptized Regularized Ratios, that serve to effectively remove unwanted singular values that may lead to poor reconstructions. This is achieved through the use of a sophisticated algorithm that progressively adjusts an initially set moderate tolerance. 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.

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참고문헌

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