Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-27T23:16:56.897Z Has data issue: false hasContentIssue false
  • English
  • Français

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:[email protected]
Email address:[email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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