Cubic-Spline Expansion with GA for Half-Space Inverse Problems
Keywords:
Cubic-Spline Expansion with GA for Half-Space Inverse ProblemsAbstract
In this paper we address an inverse scattering problem whose aim is to determine the geometrical as well as the physical properties of a perfectly conducting cylindrical body buried in a halfspace. We use cubic-spline method instead of trigonometric series to describe our shape and reformulated into an optimization problem and solved by the genetic algorithm. The genetic algorithm is employed to find out the global extreme solution of the object function. As a result, the shape of the scatterer, which is described by using cubic-spline, can be reconstructed. In such a case, fourier series expansion will fail. Even when the initial guess is far away from the exact one, the cubic-spline description and genetic algorithm can avoid the local extreme and converge to a global extreme solution. Numerical results are given to show that the shape description using cubic-spline method is much better than the Fourier series.
Downloads
References
A. Roger, “Newton-Kantorovitch algorithm applied to an
electromagnetic inverse problem,” IEEE Trans.
Antennas Propagat., vol. AP-29, pp. 232-238, Mar. 1981.
C. C. Chiu and y. W. Kiang, “inverse scattering of a
buried conducting cylinder,”Inverse Problems, vol. 7,
pp. 187-202, April 1991.
C. C. Chiu and y. W. Kiang, “microwave imaging of
multiple conducting cylinders,” IEEE Trans. Antennas
propagat., vol. 40, pp. 933-941, Aug. 1992.
G. P. Otto and W. C. Chew, “Microwave inverse
scattering-local shape function imaging for improved
resolution of strong scatterers.” IEEE Trans. Microwave
Theory Tech., vol. 42, pp. 137-142, Jan. 1994.
Kress R. “A Newton method in inverse obstacle
scattering Inverse Problem in Engineering Mechanics,”
ed H D Bui et al (Rotterdam: Balkema), pp. 425-432,
D. Colton and P. Monk, “A novel method for solving the
inverse scattering problem for time-harmonic acoustic
waves in the resonance region II,” SIAM J. Appl. Math.,
vol. 46, pp. 506-523, June 1986.
A. Kirsch, R. Kress, P. Monk, and A. Zinn, “Two
methods for solving the inverse acoustic scattering
problem, “ Inverse Problems, vol. 4, pp. 749-770, Aug.
F. Hettlich, “Two methods for solving an inverse
conductive scattering problem,” Inverse Problems, vol.
, pp. 375-385, 1994.
R. E. Kleinman and P. M. Van Den Berg, “Two-
dimensional location and shape reconstruction,” Radio
Sci., vol. 29, pp. 1157-1169, July-Aug. 1994.
T. Hohage, “Iterative methods in inverse obstacle
scattering: regularization theory of linear and nonlinear
exponentially ill-posed problems,” Dissertation Linz,
D. E. Goldgreg, Genetic Algorithm in Search,
Optimization and Machine Learning, Addison-Wesley,
C. C. Chiu and P. T. Liu, “Image reconstruction of a
perfectly conducting cylinder by the genetic algorithm,”
IEE Proc.-Micro. Antennas Propagat., vol. 143, pp. 249-
, June 1996.
T. Takenaka and Z. Q. Meng, T. Tanaka, W. C. Chew
“Local shape function combined with genetic algorithm
applied to inverse scattering for strips”, Microwave and
Optical Technology Letters, vol. 16, pp. 337-341, Dec.
Z. Q. Meng, T. Takenaka and T. Tanaka, “Image
reconstruction of two-dimensional impenetrable objects
using genetic algorithm”, Journal of Electromagnetic
Waves and Applications, vol. 13, pp. 95-118, 1999.
Y. Zhou and H. Ling “Electromagnetic inversion of
Ipswich objects with the use of the genetic algorithm”,
Microwave and Optical Technology Letters, vol. 33, pp.
-459, June 2002.
W. Chien, “Using the Genetic Algorithm to reconstruct
the two-dimensional conductor” Master Thesis, National
Tamkang University, Department of Electrical
Engineering, June 1999.
Y. Zhou, J. Li and H. Ling; “Shape inversion of metallic
cavities using hybrid genetic algorithm combined with
tabu list”, Electronics Letters, vol. 39, pp. 280 -281, Feb.
A. Qing “An experimental study on electromagnetic
inverse scattering of a perfectly conducting cylinder by
using the real-coded genetic algorithm”, Microwave and
Optical Technology Letters, vol. 30, pp. 315-320, Sept.
1
F. M. Tesche, “On the inclusion of loss in time domain
solutions of electromagnetic interaction problems,”
IEEE Trans. Electromagn. Compat., vol. 32, pp. 1-4,
E. C. Jordan and K. G. Balmain, Electromagnetic Waves
and Radiating systems. Englewood Cliffs, NJ: Prentice-
Hall, 1968.
S. Nakamura, “Applied Numerical Method in C,”
Prentice-Hall int. 1993.
”A pratical Guide to Splines,” New York: Spring-Verlag,
