Geodesic
Reconstruction algorithms for an inverse medium problem
Applications of Mathematics, Tome 63 (2018) no. 2, pp. 195-216 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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},
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     year = {2018},
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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

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