Multigrid Optimization Method Applied to Electromagnetic Inverse Scattering Problem

Mitsuru TANAKA; Kazuki YANO; Hiroyuki YOSHIDA; Atsushi KUSUNOKI

doi:10.1093/ietele/e90-c.2.320

Multigrid Optimization Method Applied to Electromagnetic Inverse Scattering Problem

Mitsuru TANAKA, Kazuki YANO, Hiroyuki YOSHIDA, Atsushi KUSUNOKI

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An iterative reconstruction algorithm of accelerating the estimation of the complex relative permittivity of a cylindrical dielectric object based on the multigrid optimization method (MGOM) is presented. A cost functional is defined by the norm of a difference between the scattered electric fields measured and calculated for an estimated contrast function, which is expressed as a function of the complex relative permittivity of the object. Then the electromagnetic inverse scattering problem can be treated as an optimization problem where the contrast function is determined by minimizing the cost functional. We apply the conjugate gradient method (CGM) and the frequency-hopping technique (FHT) to the minimization of the cost functional, and also employ the multigrid method (MGM) with a V-cycle to accelerate the rate of convergence for getting the reconstructed profile. The reconstruction scheme is called the multigrid optimization method. Computer simulations are performed for lossy and inhomogeneous dielectric circular cylinders by using single-frequency or multifrequency scattering data. The numerical results demonstrate that the rate of convergence of the proposed metod is much faster than that of the conventional CGM for both noise-free and noisy cases.

Publication: IEICE TRANSACTIONS on Electronics Vol.E90-C No.2 pp.320-326

Publication Date: 2007/02/01

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Online ISSN: 1745-1353

DOI: 10.1093/ietele/e90-c.2.320

Type of Manuscript: Special Section PAPER (Special Section on Recent Progress in Electromagnetic Theory and Its Application)

Category: Inverse Problems

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Mitsuru TANAKA, Kazuki YANO, Hiroyuki YOSHIDA, Atsushi KUSUNOKI, "Multigrid Optimization Method Applied to Electromagnetic Inverse Scattering Problem" in IEICE TRANSACTIONS on Electronics, vol. E90-C, no. 2, pp. 320-326, February 2007, doi: 10.1093/ietele/e90-c.2.320.
Abstract: An iterative reconstruction algorithm of accelerating the estimation of the complex relative permittivity of a cylindrical dielectric object based on the multigrid optimization method (MGOM) is presented. A cost functional is defined by the norm of a difference between the scattered electric fields measured and calculated for an estimated contrast function, which is expressed as a function of the complex relative permittivity of the object. Then the electromagnetic inverse scattering problem can be treated as an optimization problem where the contrast function is determined by minimizing the cost functional. We apply the conjugate gradient method (CGM) and the frequency-hopping technique (FHT) to the minimization of the cost functional, and also employ the multigrid method (MGM) with a V-cycle to accelerate the rate of convergence for getting the reconstructed profile. The reconstruction scheme is called the multigrid optimization method. Computer simulations are performed for lossy and inhomogeneous dielectric circular cylinders by using single-frequency or multifrequency scattering data. The numerical results demonstrate that the rate of convergence of the proposed metod is much faster than that of the conventional CGM for both noise-free and noisy cases.
URL: https://globals.ieice.org/en_transactions/electronics/10.1093/ietele/e90-c.2.320/_p

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@ARTICLE{e90-c_2_320,
author={Mitsuru TANAKA, Kazuki YANO, Hiroyuki YOSHIDA, Atsushi KUSUNOKI, },
journal={IEICE TRANSACTIONS on Electronics},
title={Multigrid Optimization Method Applied to Electromagnetic Inverse Scattering Problem},
year={2007},
volume={E90-C},
number={2},
pages={320-326},
abstract={An iterative reconstruction algorithm of accelerating the estimation of the complex relative permittivity of a cylindrical dielectric object based on the multigrid optimization method (MGOM) is presented. A cost functional is defined by the norm of a difference between the scattered electric fields measured and calculated for an estimated contrast function, which is expressed as a function of the complex relative permittivity of the object. Then the electromagnetic inverse scattering problem can be treated as an optimization problem where the contrast function is determined by minimizing the cost functional. We apply the conjugate gradient method (CGM) and the frequency-hopping technique (FHT) to the minimization of the cost functional, and also employ the multigrid method (MGM) with a V-cycle to accelerate the rate of convergence for getting the reconstructed profile. The reconstruction scheme is called the multigrid optimization method. Computer simulations are performed for lossy and inhomogeneous dielectric circular cylinders by using single-frequency or multifrequency scattering data. The numerical results demonstrate that the rate of convergence of the proposed metod is much faster than that of the conventional CGM for both noise-free and noisy cases.},
keywords={},
doi={10.1093/ietele/e90-c.2.320},
ISSN={1745-1353},
month={February},}

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TY - JOUR
TI - Multigrid Optimization Method Applied to Electromagnetic Inverse Scattering Problem
T2 - IEICE TRANSACTIONS on Electronics
SP - 320
EP - 326
AU - Mitsuru TANAKA
AU - Kazuki YANO
AU - Hiroyuki YOSHIDA
AU - Atsushi KUSUNOKI
PY - 2007
DO - 10.1093/ietele/e90-c.2.320
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E90-C
IS - 2
JA - IEICE TRANSACTIONS on Electronics
Y1 - February 2007
AB - An iterative reconstruction algorithm of accelerating the estimation of the complex relative permittivity of a cylindrical dielectric object based on the multigrid optimization method (MGOM) is presented. A cost functional is defined by the norm of a difference between the scattered electric fields measured and calculated for an estimated contrast function, which is expressed as a function of the complex relative permittivity of the object. Then the electromagnetic inverse scattering problem can be treated as an optimization problem where the contrast function is determined by minimizing the cost functional. We apply the conjugate gradient method (CGM) and the frequency-hopping technique (FHT) to the minimization of the cost functional, and also employ the multigrid method (MGM) with a V-cycle to accelerate the rate of convergence for getting the reconstructed profile. The reconstruction scheme is called the multigrid optimization method. Computer simulations are performed for lossy and inhomogeneous dielectric circular cylinders by using single-frequency or multifrequency scattering data. The numerical results demonstrate that the rate of convergence of the proposed metod is much faster than that of the conventional CGM for both noise-free and noisy cases.
ER -