Applications of Mathematics, Vol. 63, No. 2, pp. 195-216, 2018
Reconstruction algorithms for an inverse medium problem
Ji-Chuan Liu
Received April 27, 2017. First published March 20, 2018.
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.
Keywords: inverse medium problem; Levenberg-Marquardt algorithm; trust-region-reflective algorithm; ill-posed problem
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Affiliations: Ji-Chuan Liu, School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China, e-mail: liujichuan2003@126.com
