Multigrid Optimization Method Applied to Electromagnetic Inverse Scattering Problem

Mitsuru TANAKA
Kazuki YANO
Hiroyuki YOSHIDA
Atsushi KUSUNOKI

Publication
IEICE TRANSACTIONS on Electronics   Vol.E90-C    No.2    pp.320-326
Publication Date: 2007/02/01
Online ISSN: 1745-1353
DOI: 10.1093/ietele/e90-c.2.320
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Section on Recent Progress in Electromagnetic Theory and Its Application)
Category: Inverse Problems
Keyword: 
electromagnetic inverse scattering,  multigrid optimization method,  convergence acceleration,  iterative reconstruction algorithm,  

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Summary: 
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.