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为了重建二维有耗色散介质的电参数分布,基于Debye模型,应用泛函分析和变分法,提出一种时域逆散射新方法.该方法首先以最小二乘准则构造目标函数,将逆问题表示为约束最小化问题;接着应用罚函数法转化为无约束最小化问题;然后基于变分计算导出闭式的Lagrange函数关于特征参数的Fréchet导数;最后借助梯度算法和时域有限差分法迭代反演Debye模型参数.为了对抗噪声污染和逆问题的病态特性,采用了一阶Tikhonov正则化方法.数值应用中,利用Polak-Ribière-Polyak非线性共轭梯度法,对二维乳房模型进行了数值测试,测试结果显示了算法的可行性。
In order to reconstruct the electrical parameter distribution of two-dimensional dissipative dissipative media, a new time-domain inverse scattering method is proposed based on Debye model and functional analysis and variational method. The method first constructs the objective function with the least square criterion, The problem is expressed as the constraint minimization problem; then the penalty function method is used to convert it into an unconstrained minimization problem; then the closed Lagrange’s function Fréchet derivative of the characteristic parameters is derived based on the variational calculation; finally, the gradient algorithm and the finite-difference time-domain method To inverse Debye model parameters, a first-order Tikhonov regularization method was adopted to combat the noise pollution and the ill-posedness of the inverse problem. In the numerical application, a two-dimensional breast model was performed using the Polak-Ribière-Polyak nonlinear conjugate gradient method Numerical test, the test results show the feasibility of the algorithm.