An eigenvalue method using multiple frequency data for inverse scattering problems

Dirichlet and transmission eigenvalues have important applications in qualitative methods in inverse scattering. Motivated by the fact that these eigenvalues can be obtained from scattering data, we propose a new eigenvalue method using multiple frequency data (EM2F). The method detects eigenvalues and builds indicator functions to reconstruct the support of the target. Numerical reconstruction is quite satisfactory. Dirichlet or transmission eigenvalues are estimated. Furthermore, reconstruction of D and estimation of eigenvalues can be combined together to distinguish between the sound-soft obstacle and non-absorbing inhomogeneous medium.