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首先从体等效原理出发，得到一个积分方程组，该方程组将目标的介电常数与目标内总场及接收点上的散射场联系起来．随后，对该方程组求变分，寻求散射场对目标介电参数的梯度方向，得到反演方程．文中列举了几个典型反演实例，考察了方法的收敛速度、运行时间及对复杂目标的适应能力等因素，所得结果相当令人满意．为了尽量与实际探测接近，文中还讨论了方法抗随机噪声的能力，模拟表明，该方法具有相当强的抗噪声性能．
First of all, from the principle of volume equivalence, an integral equation system is obtained, which associates the target dielectric constant with the scattering field of the total field and the receiving point within the target. Then, the equations are variationally investigated, and the gradient direction of the scattering field to the target dielectric parameter is sought, and the inversion equation is obtained. Several typical inversion examples are listed in this paper. The convergence speed, running time and adaptability to complex targets are investigated. The obtained results are quite satisfactory. In order to try to be close to the actual detection, the paper also discusses the ability of the method to resist random noise. The simulation shows that this method has quite strong anti-noise performance.