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Adaptive eigenspace regularization for inverse scattering problems

Grote, Marcus and Nahum, Uri. (2017) Adaptive eigenspace regularization for inverse scattering problems. Preprints Fachbereich Mathematik, 2017 (10).

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Official URL: https://edoc.unibas.ch/69934/

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Abstract

A nonlinear optimization method is proposed for inverse scattering problems in the frequency domain, when the unknown medium is characterized by one or several spatially varying parameters. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type method combined with frequency stepping. Instead of a grid-based discrete representation, each parameter is projected to a separate finite-dimensional subspace, which is iteratively adapted during the optimization. Each subspace is spanned by the first few eigenfunctions of a linearized regularization penalty functional chosen a priori. The (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Numerical results illustrate the accuracy and efficiency of the resulting adaptive eigenspace regularization for single and multi-parameter problems, including the well-known Marmousi problem from geophysics.
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 Nahum, Uri
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:20 Apr 2019 15:17
Deposited On:28 Mar 2019 09:51

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