A Joint Inversion Approach of Electromagnetic and Acoustic Data Based on Pearson Correlation Coefficient

The electromagnetic (EM) inverse scattering problems (ISPs) exhibit strong nonlinearity, making it a challenge to reconstruct the relative permittivity of strong scatterers with high quality. Joint inversion can leverage the satisfactory solution obtained from acoustic inversion to mitigate the impact of strong nonlinearity on EM inversion. However, how to improve the precision of reconstructing the internal electrical parameter distribution through this kind of joint inversion approach is still a challenge. Aiming to improve the quality of reconstruction, a new joint inversion method based on the framework of the subspace-based optimization method (SOM) is proposed in this article. This new method utilizes the Pearson correlation coefficient (PCC) to construct structural similarity constraints, thereby enhancing the linear correlation between EM and acoustic parameters. In the inversion process, all data obtained from acoustic inversion can offer effective constraints. In order to improve the convergence speed and stability of the proposed method, a constraint that consists of cross-gradient function (CGF) is induced in the object function. By utilizing the results of the results of acoustic inversion, the inversion domain can be further refined, giving rise to better computational efficiency. With these treatments, the proposed method has a better performance in both accuracy and efficiency. The effectiveness and advantages of the proposed method are validated through several numerical examples.