变分自编码器在电磁逆散射问题中的应用研究

      A Study on the Application of Variational Autoencoders to Electromagnetic Inverse Scattering Problems

      • 摘要: 为缓解逆散射问题的病态性并提升重建精度,本文引入生成式先验信息,系统研究不同生成模型驱动的反演策略对重建效果的影响。首先,通过微调Stable Diffusion的变分自编码器 (variational autoencoder, VAE) 参数,构建了适配逆散射任务的VAE模型。随后,在基于对比源预测算子和VAE的框架下,提出了三种基于VAE的反演策略:固定级联策略、微调级联策略和像素投影策略。通过合成数据和实测数据,对三种策略在重建精度、抗噪鲁棒性和计算效率方面的表现进行了系统评估。结果表明,三种策略均能有效降低逆问题的病态性,提升反演效果。固定级联策略具有较高的计算效率,微调级联策略通过调整生成模型参数进一步提升反演精度,像素投影策略在复杂场景下具有更优的重建质量和稳定性。研究表明,合理利用生成模型能有效融合先验信息,显著提升反演精度,为电磁成像提供准确而鲁棒的解决方案。

         

        Abstract: To mitigate the inherent ill-posedness of inverse scattering problems and improve reconstruction accuracy, this paper introduces generative priors and systematically investigates the influence of various generative model driven inversion strategies on reconstruction performance. Initially, a variational autoencoder (VAE) tailored for inverse scattering tasks is developed by fine-tuning the VAE parameters of Stable Diffusion. Subsequently, within a framework integrating contrast source prediction operators with VAE, three inversion strategies are proposed: frozen cascade strategy, fine-tuned cascade strategy, and pixel projection strategy. The performance of these strategies is systematically evaluated using synthetic and experimental data, focusing on reconstruction accuracy, noise robustness, and computational efficiency. Numerical results show that all three strategies effectively alleviate the ill-posedness of the inverse problem and enhance reconstruction quality. The frozen cascade strategy offers higher computational efficiency, the fine-tuned cascade strategy improves reconstruction accuracy by adjusting generative model parameters, and the pixel projection strategy provides superior reconstruction quality and stability in complex scenarios. This study demonstrates that effective integration of generative models enables the incorporation of prior information, significantly improving inversion accuracy and offering a reliable and robust solution for electromagnetic imaging.

         

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