A Modified Contrast Source Inversion Method for Electrically Dispersive Media

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

Abstract

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

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.

Figures/Tables 6

Fig.1 Geometric model of an electromagnetic inverse scattering problem

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

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

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

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

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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