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

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

Yaakov Olshansky 1*, Eli Turkel 1

1 Applied Mathematics, Tel-Aviv University, Israel.

Received 18 November 2009; Accepted (in revised version) 1 December 2010
Available online 24 October 2011


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 $\widetilde{u}_{\infty}$ is a perturbation of the FFP then we attempt to find $\Gamma$, the scatterer shape, which minimizes $\parallel u_{\infty}-\widetilde{u}_{\infty} \parallel$ using the conjugate gradient method for the denoised FFP.

AMS subject classifications: 81U40

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Key words: Scattering inverse problem, far field pattern.

*Corresponding author.
Email: (Y. Olshansky), (E. Turkel)

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