In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate the impedance of the total field at multiple frequencies to derivatives of the potential. Using this trace formula we obtain a system of coupled differential equations which can be solved to obtain the potential in a stable manner. Finally, the performance of the reconstruction algorithm is illustrated with several numerical examples.

翻译：本文提出了一种基于多频数据求解径向对称区域内亥姆霍兹方程逆问题的方法。该方法通过构建适当的迹公式，将多个频率下总场的阻抗与势函数的导数联系起来。利用该迹公式，我们获得了一个可稳定求解势函数的耦合微分方程组。最后，通过多个数值算例验证了该重建算法的有效性。