  In this paper, we improved the performance of the contrast source inversion
(CSI) method by incorporating a so-called cross-correlated cost functional,
which interrelates the state error and the data error in the measurement
domain. The proposed method is referred to as the cross-correlated CSI. It
enables better robustness and higher inversion accuracy than both the classical
CSI and multiplicative regularized CSI (MR-CSI). In addition, we show how the
gradient of the modified cost functional can be calculated without
significantly increasing the computational burden. The advantages of the
proposed algorithms are demonstrated using a 2-D benchmark problem excited by a
transverse magnetic wave as well as a transverse electric wave, respectively,
in comparison to classical CSI and MR-CSI.
