# A Phaseless Source Reconstruction Method Based on Adam Optimization Algorithm Combined with Regularization

## TL;DR

This paper introduces a new method for solving electromagnetic source reconstruction by combining Adam optimization and regularization to improve accuracy and noise resistance.

## Contribution

A novel phaseless source reconstruction method using Adam optimization and L2 regularization is proposed to overcome ill-conditioning and local optima issues.

## Key findings

- The method avoids ill-conditioned matrix inversion using Adam optimization, improving reconstruction accuracy.
- L2 regularization enhances anti-noise performance and prevents local optima in dipole solutions.
- Simulations and experiments confirm the effectiveness of the proposed approach.

## Abstract

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.