Reconstruction algorithms for an inverse medium problem

[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.

[学科分类] 应用数学

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