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Volume 11, Issue 2
Simultaneous Scatterer Shape Estimation and Partial Aperture Far-Field Pattern Denoising

Yaakov Olshansky & Eli Turkel

DOI: 10.4208/cicp.181109.011210s

Commun. Comput. Phys., 11 (2012), pp. 271-284.

Published online: 2012-12

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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 ‖ u∞−ũ∞ ‖ using the conjugate gradient method for the denoised FFP.

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@Article{CiCP-11-271, author = {Yaakov Olshansky and Eli Turkel}, title = {Simultaneous Scatterer Shape Estimation and Partial Aperture Far-Field Pattern Denoising}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {2}, pages = {271--284}, 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 ‖ u∞−ũ∞ ‖ using the conjugate gradient method for the denoised FFP.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.181109.011210s}, url = {http://global-sci.org/intro/article_detail/cicp/7361.html} }
TY - JOUR T1 - Simultaneous Scatterer Shape Estimation and Partial Aperture Far-Field Pattern Denoising AU - Yaakov Olshansky & Eli Turkel JO - Communications in Computational Physics VL - 2 SP - 271 EP - 284 PY - 2012 DA - 2012/12 SN - 11 DO - http://doi.org/10.4208/cicp.181109.011210s UR - https://global-sci.org/intro/article_detail/cicp/7361.html KW - AB -

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 ‖ u∞−ũ∞ ‖ using the conjugate gradient method for the denoised FFP.

Yaakov Olshansky and Eli Turkel. (2012). Simultaneous Scatterer Shape Estimation and Partial Aperture Far-Field Pattern Denoising. Communications in Computational Physics. 11 (2). 271-284. doi:10.4208/cicp.181109.011210s
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