Adaptive Eigenspace for Multi-Parameter Inverse Scattering Problems

Grote, Marcus J. and Nahum, Uri. (2019) Adaptive Eigenspace for Multi-Parameter Inverse Scattering Problems. Computers & mathematics with applications, 77 (12). pp. 3264-3280.

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Official URL: https://edoc.unibas.ch/75283/

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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 model from geosciences.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Numerik (Grote)
UniBasel Contributors:Grote, Marcus J. and Nahum, Uri
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:06 Jul 2020 14:56
Deposited On:24 Jun 2020 15:20

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