一种电色散媒质的改进对比源反演方法

doi:10.19596/j.cnki.1001-246x.8506

摘要/Abstract

摘要：

基于一种单极德拜(Debye)经验模型, 尝试改进其中的一种多频乘性正则化对比源反演方法, 改进的主要思路是: 从直接反演电参数差异, 改进为间接反演4种频率无关的模型参数, 即光频相对介电常数、相对介电常数差、静态电导率和弛豫时间。两个数值算例的仿真结果初步证实了改进方法的可行性和鲁棒性。

关键词: 电磁逆散射, 对比源反演, 德拜色散媒质, 乘性正则化

Abstract:

Based on a single-pole Debye empirical formula, a multi frequency contrast source inversion (CSI) approach with a multiplicative regularization term is improved tentatively. The main improvement is a modification of inversion object from direct estimation of contrast between Debye scatterers and background medium to indirect reconstruction of four kinds of frequency-independent one-pole Debye model parameters, i.e., the optical relative permittivity, relative permittivity difference, static conductivity, and relaxation time. Two numerical examples confirmed preliminarily feasibility and robustness of the improved method.

Key words: electromagnetic inverse scattering, contrast source inversion (CSI), Debye dispersive media, multiplicative regularization

刘广东, 张开银. 一种电色散媒质的改进对比源反演方法[J]. 计算物理, 2022, 39(6): 699-706.

Guangdong LIU, Kaiyin ZHANG. A Modified Contrast Source Inversion Method for Electrically Dispersive Media[J]. Chinese Journal of Computational Physics, 2022, 39(6): 699-706.

图/表 6

图1 电磁逆散射问题的几何模型

Fig.1 Geometric model of an electromagnetic inverse scattering problem

图2 单极Debye模型参数分布(a) ε∞真实值；(b) ε∞重建值；(c) Δε真实值；(d) Δε重建值；(e) σs真实值；(f) σs重建值；(g) τ真实值；(h) τ重建值

Fig.2 Distribution of single-pole Debye parameters (a) true ε∞; (b) reconstructed ε∞; (c) true Δε; (d) reconstructed Δε; (e) true σs; (f) reconstructed σs; (g) true τ; (h) reconstructed τ

图3 算例1迭代过程反演结果(ε∞、Δε、σs、τ)的归一化相对均方根误差

Fig.3 Normalized relative root mean squared errors of reconstructed results (ε∞, Δε, σs, and τ) versus the number of iterations in Example 1

表1 在0.5 ~ 20.0 GHz拟合的乳房模型各组织的单极Debye模型参数

Table 1 Parameters of breast tissues in a single-pole Debye model fitted from 0.5 to 20.0 GHz

	ε_∞	Δε	σ_s/(S·m^-1)	τ/ps
Maximum	7.12	59.03	1.41	8.48
Group1-high	8.97	44.61	0.83	10.85
Group1-median	10.08	38.52	0.73	11.21
Group1-low	10.04	26.48	0.46	10.93
Group3-high	4.22	3.38	0.086	14.56
Group3-median	3.23	1.57	0.037	15.10
Group3-low	2.98	1.09	0.021	17.20
Minimum	2.32	0.097	0.002 4	17.83
Skin (dry)	6.97	32.03	0.75	8.68
Muscle	11.90	41.62	0.83	9.04

图4 基于磁共振成像的二维癌变乳房各单极Debye模型参数的真实分布、最终重建分布、通过肿瘤中心抽取的沿x轴向分布(a)~(c) ε∞；(d)~(f) Δε；(g)~(i) σs；(j)~(l) τ

Fig.4 Ground truth, reconstructed results at the 100th iteration, and their distributions along the x axis through the center of the tumor (A MRI-based 2-D cancerous breast phantom with one tumor) (a)-(c) optical relative permittivity ε∞; (d)-(f) relative permittivity difference Δε; (g)-(i) static conductivity σs; (j)-(l) relaxation time τ, respectively

图5 算例2迭代过程反演结果(ε∞、Δε、σs、τ)的归一化相对均方根误差

Fig.5 Normalized relative root mean squared errors of reconstructed results (ε∞, Δε, σs, and τ) versus the number of iterations in Example 2

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