Using the linear sampling method and an improved maximum product criterion for the solution of the electromagnetic inverse medium problem

We present a Tikhonov parameter choice approach for three-dimensional reconstructions based on a maximum product criterion (MPC) which provides a regularization parameter located in the concave part of the L-curve in log-log scale. Our method, baptized Improved Maximum Product Criterion (IMPC), is an extension of the MPC method developed by Bazán et al. for two-dimensional reconstructions. In the 3D framework, IMPC computes the regularization parameter via a fast iterative algorithm and requires no a priori knowledge of the noise level in the data. It is applied on the linear sampling method for solving the electromagnetic inverse medium problem in the 3D framework. The effectiveness of IMPC is illustrated with numerical examples involving more than one scatterer.