Comparison among the variants of subspace-based optimization method for addressing inverse scattering problems: transverse electric case

Li Pan; Xudong Chen; Yu Zhong; Swee Ping Yeo

doi:10.1364/JOSAA.27.002208

Journal of the Optical Society of America A
Vol. 27,
Issue 10,
pp. 2208-2215
(2010)
•https://doi.org/10.1364/JOSAA.27.002208

Comparison among the variants of subspace-based optimization method for addressing inverse scattering problems: transverse electric case

Li Pan, Xudong Chen, Yu Zhong, and Swee Ping Yeo

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Li Pan, Xudong Chen, Yu Zhong, and Swee Ping Yeo, "Comparison among the variants of subspace-based optimization method for addressing inverse scattering problems: transverse electric case," J. Opt. Soc. Am. A 27, 2208-2215 (2010)

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Abstract

The subspace-based optimization method (SOM) is an efficient approach to addressing the inverse scattering problem. In this paper, a comparative study, on the basis of numerical experiments, is conducted to evaluate the performances of variants of SOM, so as to find the optimal method for the determination of the ambiguous portion, which has a dominant influence on the computational cost and the reconstruction capability of the algorithm.

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Variable Name	Size	Meaning
${\bar{E}}_{p}^{inc}$	$2 N_{d} \times 1$	Electrical field incident into the scatter from the $p th$ transmitting antenna
${\bar{E}}_{p}^{scat}$	$2 N_{r} \times 1$	Scattered electrical field due to $p th$ incidence
${\bar{I}}_{p}^{d}$	$2 N_{d} \times 1$	Induced contrast displacement current due to $p th$ incidence
$\bar{\bar{ξ}}$	$2 N_{d} \times 2 N_{d}$	Diagonal matrix of scattering strength
${\bar{\bar{G}}}_{S}$	$2 N_{r} \times 2 N_{d}$	Green’s function matrix describing the scattering from object to the receiving antennas
${\bar{\bar{G}}}_{D}$	$2 N_{d} \times 2 N_{d}$	Green’s function matrix describing the multiple scattering effect

	Original SOM		CSI-like SOM		New Variant of SOM
	Number of iterations	Time per iteration (s)	Number of iterations	Time per iteration (s)	Number of iterations	Time per iteration (s)
Experiment 1	10	17.4	28	0.14	19	0.84
Experiment 2	7	17.7	30	0.14	23	0.82
Experiment 3	5	16.5	9	0.13	7	0.64
Experiment 4	15	211	18	0.91	40	4.3
Experiment 5	6	267	12	0.92	8	4.5
Experiment 6	12	256	40	0.93	30	4.6

Variable Name	Size	Meaning
${\bar{E}}_{p}^{inc}$	$2 N_{d} \times 1$	Electrical field incident into the scatter from the $p th$ transmitting antenna
${\bar{E}}_{p}^{scat}$	$2 N_{r} \times 1$	Scattered electrical field due to $p th$ incidence
${\bar{I}}_{p}^{d}$	$2 N_{d} \times 1$	Induced contrast displacement current due to $p th$ incidence
$\bar{\bar{ξ}}$	$2 N_{d} \times 2 N_{d}$	Diagonal matrix of scattering strength
${\bar{\bar{G}}}_{S}$	$2 N_{r} \times 2 N_{d}$	Green’s function matrix describing the scattering from object to the receiving antennas
${\bar{\bar{G}}}_{D}$	$2 N_{d} \times 2 N_{d}$	Green’s function matrix describing the multiple scattering effect

	Original SOM		CSI-like SOM		New Variant of SOM
	Number of iterations	Time per iteration (s)	Number of iterations	Time per iteration (s)	Number of iterations	Time per iteration (s)
Experiment 1	10	17.4	28	0.14	19	0.84
Experiment 2	7	17.7	30	0.14	23	0.82
Experiment 3	5	16.5	9	0.13	7	0.64
Experiment 4	15	211	18	0.91	40	4.3
Experiment 5	6	267	12	0.92	8	4.5
Experiment 6	12	256	40	0.93	30	4.6

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Journal of the Optical Society of America A