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Adaptive eigenspace method for inverse scattering problems in the frequency domain

Grote, Marcus and Kray, Marie and Nahum, Uri. (2016) Adaptive eigenspace method for inverse scattering problems in the frequency domain. Preprints Fachbereich Mathematik, 2016 (13).

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Abstract

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Numerik (Grote)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Grote, Marcus J. and Kray, Marie and Nahum, Uri
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:22 Apr 2019 14:40
Deposited On:28 Mar 2019 09:51

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