非均匀背景中的电磁逆散射研究

Electromagnetic inverse scattering is one of the most important problems in the electromagnetic research. It is a typical non-linear ill posed problem, which is ill-conditioned. The accuracy of the solutions usually depends on both the quality and quantity of the available information, while the quality and quantity are usually insufficient in most cases. In order to obtain a steady and accurate inversion, an inhomogeneous background is employed, which is regarded as adding some apriori information, in order to get more and better information of the target. First, a modeling method of the inhomogeneous backgrounds is studied, and a new signal calibration method and regularization method will be presented here. Then an evaluation method of the inhomogeneous backgrounds is studied, which is used to evaluate both the direction and scope of the influence to the solving of electromagnetic inverse scattering problem when an inhomogeneous background is employed. On this basis, we turn to the method of designing an optimal inhomogeneous background. This project aims to provide a potential method of using the inhomogeneous background in the electromagnetic inverse scattering problem. In the proposed method, the inhomogeneous background is treated as the apriori information and taken into the inversion algorithm, the apriori information involved here is not relate to the target, so that, the non-physical or artificial constraints, which would affect the problem solving can be avoided. The method proposed can reduce the ill condition of an electromagnetic inverse scattering problem without changing the hardware system we have. Furthermore, it can make the solution more accurate and got more quickly.

电磁逆散射问题是电磁学的重要研究领域，是一种典型的非线性不适定问题，具有病态性。其解的准确度通常依赖于可用信息的质和量，而可用信息往往是质和量均不足的，为了获得稳定准确的反演结果，我们使用特定的非均匀背景作为先验信息来获取更多更好的目标信息。本课题首先研究非均匀背景的建模方法，给出一种新的信号校准方法和正则化方法。然后研究非均匀背景的评价方法，用以评价非均匀背景对电磁逆散射问题的作用方向和影响大小。最后，在此基础上研究最优非均匀背景的设计方法。本课题的研究目的是提供一种电磁逆散射问题中应用非均匀背景的方法，该方法将非均匀背景作为先验信息引入，此类先验信息不依赖于目标本身，可以避免计算过程中引入非物理或人为的约束而影响求解过程。该方法可以在不改变现有硬件系统的情况下降低电磁逆散射问题的病态性，并使求解更加准确且快速。

本课题针对电磁逆散射问题中信息的质和量均不足而导致求解困难、结果不稳定等问题，提出使用特定的非均匀背景作为先验信息来获取更多更好的目标信息的方法来增强电磁逆散射。首先研究非均匀背景的建模方法，给出了电磁逆散射问题求解方法和积分算子的分析方法。然后研究非均匀背景的评价方法，将非均匀背景纳入积分算子中，对积分算子进行分析，提出一种评价度量对积分算子进行评价，从而预测该非均匀背景对逆散射问题求解的影响。最后，在此基础上研究了最优非均匀背景的设计方法。本课题的研究目的是提供一种电磁逆散射问题中应用非均匀背景的方法，该方法将非均匀背景作为先验信息引入，此类先验信息不依赖于目标本身，可以避免计算过程中引入非物理或人为的约束而影响求解过程。该方法可以为电磁逆散射领域的研究提供一些参考。