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本文提出自由空间中二维介质柱微波成像的新方法一变分迭代法（VIM），详细考察了它的性能．并从理论上分析了它相比其它同类成像方法性能明显优越的原因，为今后进一步提高它的成像性能、拓宽其适用范围提供了理论基础．我们综合利用电磁体等效原理和变分原理导出了VIM的反演方程，该方程反映了散射场的微小变化与目标介质柱介电参数微小变化之间的近似线性关系，从而反映了散射场与目标介质柱介电参数之间的非线性关系简要讨论了病态问题的正则化方法．详细考察了VIM法的收敛性能、适应复杂目标的能力、抗随机噪声干扰的能力、利用不完备测量散射信息反演目标的能力、利用单频散射信息反演目标的能力等多项反映其实用能力的性能指标，证实了方法的实用价值．
In this paper, a new method of two-dimensional media column microwave imaging in free space, a Variational Iterative Method (VIM), is proposed and its properties are investigated in detail. The reason why it is superior to other similar imaging methods is theoretically analyzed, which provides a theoretical basis for further improving its imaging performance and broadening its application range in the future. Using the principle of electromagnet equivalence and variational principle, we derive the inversion equation of VIM. The equation reflects the approximate linear relationship between the small change of the scattering field and the small change of the dielectric parameter of the target dielectric column, thus reflecting the scattering field And the dielectric parameters of the target dielectric column nonlinear relationship between a brief discussion of the regularization of pathological problems. This paper examines in detail the convergence performance of VIM, the ability to adapt to complex targets, the ability to resist random noise interference, the ability to use inaccurate measurements to retrieve targets for scattering information, the ability to retrieve targets using single- The performance index of capability confirms the practical value of the method.