In the solution of equivalent dipoles for inverse electromagnetic problems, the traditional least squares method suffers from ill-conditioned matrices, resulting in insufficient accuracy and anti-noise performance, while existing optimization algorithms tend to fall into local optima during iteration. To address these issues, this paper proposes a phaseless source reconstruction method combining the Adam optimization algorithm with L2 regularization, which can stably solve the equivalent dipole source. The proposed method uses Adam optimization to avoid the direct inversion of ill-conditioned matrices, which improves the accuracy of near-field source reconstruction and effectively avoids falling into local optima. The introduced L2 regularization further suppresses local optima and significantly enhances the anti-noise performance of the equivalent dipole solution. In addition, simulations and experiments are carried out to verify the effectiveness of the proposed method.
Ma et al. (Sun,) studied this question.