ABSTRACT

In this paper, we consider an inverse conductive scattering problem for the Helmholtz equation from measurements on the outer boundary. We want to seek reconstruction algorithms to detect the number, location, size and shape of inhomogeneities within a body. This problem is nonlinear and ill-posed, thus we should consider regularization techniques in order to improve the corresponding approximation. We examine the viability of our proposed reconstruction algorithms through the use of numerical experiments.

中文翻译：

---

亥姆霍兹方程的逆传导散射问题的重构算法

摘要

在本文中，我们从外边界的测量中考虑亥姆霍兹方程的逆传导散射问题。我们希望寻求重建算法来检测身体内不均匀性的数量、位置、大小和形状。这个问题是非线性和病态的，因此我们应该考虑正则化技术以改进相应的近似值。我们通过使用数值实验来检查我们提出的重建算法的可行性。