Inversion of Multifrequency Data With the Cross‐Correlated Contrast Source Inversion Method

Cross‐correlated contrast source inversion (CC‐CSI) is a nonlinear iterative inversion method that is proposed recently for solving the inverse scattering problems. In CC‐CSI, a cross‐correlated error is constructed and introduced to the cost functional, which improves the inversion ability when compared to the classical design of the cost functional by exploiting the mismatch between the data error and state error. In this paper, the multifrequency inversion for electromagnetic waves is considered and a multifrequency version of CC‐CSI is proposed. Numerical and experimental inversion results of both transverse magnetic and transverse electric polarization demonstrate that when multifrequency data are available, CC‐CSI still outperforms the multiplicative‐regularized CSI method in the inversion of more complicated scatterers. Plain Language Summary In the field of inverse scattering problems, the dielectric properties of unknown targets can be recovered from the scattered electromagnetic/acoustic waves. Nonlinear iterative methods are a group of such approaches in which a cost functional is minimized iteratively. The classical cost functional is designed using two terms. One is to fit the measurement data and the other one is to fit the wave equations. Recently, a cross‐correlated term was proposed in our research, and it has been demonstrated that the inversion performance is improved by considering the newly proposed term. It also implies the potential improvement for other nonlinear iterative methods. In this paper, the idea has been implemented to process the multifrequency data simultaneously. Results show that the improvement of inversion performance (e.g., the reliability) is still obvious in comparison to the state‐of‐the‐art nonlinear iterative methods in the multifrequency cases. Key Points Exploiting the frequency diversity improves the robustness and accuracy of the contrast source inversion method The reliability of the CSI method can be improved by introducing the cross‐correlated error Initial guess is still critical for the CC‐CSI method