Integral and finite-difference formulations of the contrast source inversion method

In this paper we review and discuss the contrast source inversion (CSI) methods. The contrast source inversion method is a full non-linear inversion approach where the permittivity and conductivity of unknown objects are retrieved from non-invasive electromagnetic wavefield measurements. The main attractive feature of the CSI method is its efficiency. This method does not need to explicitly solve the full forward problem in each of its iterative step. Furthermore by adding a multiplicative regularization (MR) constraint in the CSI method, the method is shown to be very robust in reconstructing objects with sharp edges. We discuss this so-called MR-CSI method, either using an integral equation formulation or a differential equation formulation.