Reconstruction algorithms for an inverse medium problem

Applications of mathematics

Ji-Chuan Liu^1¹ 

[1] School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China^1

关键词: inverse medium problem;    Levenberg-Marquardt algorithm;    trust-region-reflective algorithm;    ill-posed problem;   

DOI  :  10.21136/AM.2018.0114-17

学科分类：应用数学

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown