On the inverse scattering problem for radially-symmetric domains in two dimensions

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.