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Adaptive Eigenspace for Multi-Parameter Inverse Scattering Problems
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
 
ID 4528310
Author(s) Grote, Marcus J.; Nahum, Uri
Author(s) at UniBasel Grote, Marcus J.
Nahum, Uri
Year 2019
Title Adaptive Eigenspace for Multi-Parameter Inverse Scattering Problems
Journal Computers & mathematics with applications
Volume 77
Number 12
Pages / Article-Number 3264-3280
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 model from geosciences.
Publisher Elsevier
ISSN/ISBN 0898-1221
URL https://www.sciencedirect.com/science/article/pii/S0898122119300732?via%3Dihub
edoc-URL https://edoc.unibas.ch/75283/
Full Text on edoc No
Digital Object Identifier DOI 10.1016/j.camwa.2019.02.005
ISI-Number WOS:000471088800015
Document type (ISI) Article
 
   

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