The multi-frequency diagonalized contrast source method for electromagnetic inversion

Inverse scattering problems deal with the determination of the constitutive parameters of the unknown objects embedded in a known background medium. In this problem, the configuration is illuminated by a single frequency wave-field and the scattered field is measured in an external observation domain. The inversion of this data is well-known to be non-linear and ill-posed. Furthermore, the retrievable information is limited. In order to overcome such drawbacks, multi-frequency data can be used by exploiting the Maxwellian dispersion relationships. However, the use of the set of multi-frequency data significantly increases the computational burden of the inversion process. Recently, the so-called Diagonalized Contrast Source Inversion (DCSI) method is introduced to efficiently solve the inverse problem. In this method, instead of solving the full non-linear problem, a three-linear-step procedure is carried out to significantly reduce the overall computational time. In order to further enhance the DCSI method, in this paper it has been extended for dealing with multi-frequency data.