Geodesic
Reconstruction algorithms for an inverse medium problem
Applications of Mathematics, Tome 63 (2018) no. 2, pp. 195-216.

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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.
DOI : 10.21136/AM.2018.0114-17
Classification : 65N20, 65N21, 92C55
Keywords: inverse medium problem; Levenberg-Marquardt algorithm; trust-region-reflective algorithm; ill-posed problem 
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     author = {Liu, Ji-Chuan},
     title = {Reconstruction algorithms for an inverse medium problem},
     journal = {Applications of Mathematics},
     pages = {195--216},
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     volume = {63},
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     doi = {10.21136/AM.2018.0114-17},
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     zbl = {06890305},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0114-17/}
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Liu, Ji-Chuan. Reconstruction algorithms for an inverse medium problem. Applications of Mathematics, Tome 63 (2018) no. 2, pp. 195-216. doi : 10.21136/AM.2018.0114-17. http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0114-17/

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