二维有耗色散介质的时域逆散射方法

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

Time-domain inverse scattering problem for two-dimensional frequency-dispersive lossy media

A time-domain inverse scattering method for reconstruction of dispersive dielectric properties of two-dimensional (2D) lossy media based on the Debye model by using functional analysis and variational methods is developed. Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fréchet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations. Finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain (FDTD) method. Also, the first-order Tikhonov’s regularization is adopted to cope with noise and the ill-posedness of the problem. In numerical example, the presented algorithm is applied to a 2D breast model with the help of the Polak-Ribière-Polyak (PRP) conjugate gradient (CG) method, and the results demonstrate its feasibility.