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Simultaneous Scatterer Shape Estimation and Partial Aperture Far-Field Pattern Denoising

Published online by Cambridge University Press:  20 August 2015

Yaakov Olshansky  and
Eli Turkel
Yaakov Olshansky*
Affiliation:
Applied Mathematics, Tel-Aviv University, Israel
Eli Turkel*
Affiliation:
Applied Mathematics, Tel-Aviv University, Israel
*
Corresponding author.Email:oyakov@post.tau.ac.il
Email address:turkel@post.tau.ac.il
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Abstract

We study the inverse problem of recovering the scatterer shape from the far-field pattern(FFP) in the presence of noise. Furthermore, only a discrete partial aperture is usually known. This problem is ill-posed and is frequently addressed using regularization. Instead, we propose to use a direct approach denoising the FFP using a filtering technique. The effectiveness of the technique is studied on a scatterer with the shape of the ellipse with a tower. The forward scattering problem is solved using the finite element method (FEM). The numerical FFP is additionally corrupted by Gaussian noise. The shape parameters are found based on a least-square error estimator. If ũ∞ is a perturbation of the FFP then we attempt to find Γ, the scatterer shape, which minimizes ∣∣ũ∞ − ũ∞∣∣ using the conjugate gradient method for the denoised FFP

Keywords

81U40Scattering inverse problemfar field pattern
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 271 - 284
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Colton, D. and Kress, R., Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed., Springer-Verlag, 1998.Google Scholar
[2]Nabney, I. T., Netlab: Algorithms for Pattern Recognition, Springer Verlag, London, 2004.Google Scholar
[3]Neumaier, A., MINQ – General Definite and Bound Constrained Indefinite Quadratic Programming, WWW-Document, http://www.mat.univie.ac.at/neum/software/minq/, 1998.Google Scholar
[4]Colton, D. and Kress, R., Using fundamentalsolutions in inverse scattering, Inverse Problems, 22(3) (2006).CrossRefGoogle Scholar
[5]Kriegsmann, G. A., Traflove, A. and Umashanker, K. R., A new formulation of electromagnetic scattering using on surface radiation condition approach, IEEE Trans. Ant. Prop. AP35, 42 (1987).Google Scholar
[6]Polak, E., Computational Methods in Optimization: A Unified Approach, Academic Press, New York, 1971.Google Scholar
[7]Fletcher, R., Practical Methods of Optimization, John Wily, New York, 1987.Google Scholar
[8]Donoho, D. L., Progress in wavelet analysis and WVD: a ten minute tour, in: Progress in Wavelet Analysis and Applications, Meyer, Y., Roques, S. Eds., pp. 109–128, 1993, Frontires Ed.Google Scholar
[9]Donoho, D. L., De-noising by soft-thresholding, IEEE Trans. on Inf. Theory, 41(3) (1995), 613–627.Google Scholar
[10]Donoho, D. L., Johnstone, I. M., Kerkyacharian, G. and Picard, D., Wavelet shrinkage: asymptotia, J. Roy. Stat. Soc. Series B, 57(2) (1995).Google Scholar
[11]Donoho, D. L. and Johnstone, I. M., Ideal spatial adaptation by wavelet shrinkage, Biometrika, 81(3) (1994), 425–455.Google Scholar
[12]Antoniadis, A. and Oppenheim, G. Eds., Wavelets and Statistics, Lecture Notes in Statistics 103, Springer Verlag, 1995.Google Scholar
[13]Daubechies, I., Ten Lectures on Wavelets, SIAM, 1992.Google Scholar
[14]Vidakovic, B., Statistical Model by Wavelets, John Willey & Sons, New York, 1999.Google Scholar