Reconstruction algorithms for an inverse medium problem

Ji-Chuan Liu

Applications of Mathematics (2018)

  • Volume: 63, Issue: 2, page 195-216
  • ISSN: 0862-7940

Abstract

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In this paper, we consider a two-dimensional inverse medium problem from noisy observation data. We propose effective reconstruction algorithms to detect the number, the location and the size of the piecewise constant medium within a body, and then we try to recover the unknown shape of inhomogeneous media. This problem is nonlinear and ill-posed, thus we should consider stable and elegant approaches in order to improve the corresponding approximation. We give several examples to show the viability of our proposed algorithms.

How to cite

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Liu, Ji-Chuan. "Reconstruction algorithms for an inverse medium problem." Applications of Mathematics 63.2 (2018): 195-216. <http://eudml.org/doc/294756>.

@article{Liu2018,
abstract = {In this paper, we consider a two-dimensional inverse medium problem from noisy observation data. We propose effective reconstruction algorithms to detect the number, the location and the size of the piecewise constant medium within a body, and then we try to recover the unknown shape of inhomogeneous media. This problem is nonlinear and ill-posed, thus we should consider stable and elegant approaches in order to improve the corresponding approximation. We give several examples to show the viability of our proposed algorithms.},
author = {Liu, Ji-Chuan},
journal = {Applications of Mathematics},
keywords = {inverse medium problem; Levenberg-Marquardt algorithm; trust-region-reflective algorithm; ill-posed problem},
language = {eng},
number = {2},
pages = {195-216},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Reconstruction algorithms for an inverse medium problem},
url = {http://eudml.org/doc/294756},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Liu, Ji-Chuan
TI - Reconstruction algorithms for an inverse medium problem
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 195
EP - 216
AB - In this paper, we consider a two-dimensional inverse medium problem from noisy observation data. We propose effective reconstruction algorithms to detect the number, the location and the size of the piecewise constant medium within a body, and then we try to recover the unknown shape of inhomogeneous media. This problem is nonlinear and ill-posed, thus we should consider stable and elegant approaches in order to improve the corresponding approximation. We give several examples to show the viability of our proposed algorithms.
LA - eng
KW - inverse medium problem; Levenberg-Marquardt algorithm; trust-region-reflective algorithm; ill-posed problem
UR - http://eudml.org/doc/294756
ER -

References

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