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A greedy algorithm for nonlinear inverse problems with an application to nonlinear inverse gravimetry

Kontak, Max and Michel, Volker (2018) A greedy algorithm for nonlinear inverse problems with an application to nonlinear inverse gravimetry. GEM - International Journal on Geomathematics, 9 (2), pp. 167-198. Springer. DOI: 10.1007/s13137-018-0110-6 ISSN 1869-2672

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Official URL: https://link.springer.com/article/10.1007/s13137-018-0110-6

Abstract

Based on the Regularized Functional Matching Pursuit (RFMP) algorithm for linear inverse problems, we present an analogous iterative greedy algorithm for nonlinear inverse problems, called RFMP_NL. In comparison to established methods for nonlinear inverse problems, the algorithm is able to combine very diverse types of basis functions, for example, localized and global functions. This is important, in particular, in geoscientific applications, where global structures have to be distinguished from local anomalies. Furthermore, in contrast to other methods, the algorithm does not require the solution of large linear systems. We apply the RFMP_NL to the nonlinear inverse problem of gravimetry, where gravitational data are inverted for the shape of the surface or inner layer boundaries of planetary bodies. This inverse problem is described by a nonlinear integral operator, for which we additionally provide the Fréchet derivative. Finally, we present two synthetic numerical examples to show that it is beneficial to apply the presented method to inverse gravimetric problems.

Item URL in elib:https://elib.dlr.de/122986/
Document Type:Article
Additional Information:This is a post-peer-review, pre-copyedit version of an article published in GEM: International Journal on Geomathematics. The final authenticated version is available online at: https://link.springer.com/article/10.1007/s13137-018-0110-6.
Title:A greedy algorithm for nonlinear inverse problems with an application to nonlinear inverse gravimetry
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Kontak, MaxMax.Kontak (at) DLR.dehttps://orcid.org/0000-0003-3738-7483
Michel, VolkerUniversität Siegenhttps://orcid.org/0000-0002-2551-0491
Date:2018
Journal or Publication Title:GEM - International Journal on Geomathematics
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:9
DOI :10.1007/s13137-018-0110-6
Page Range:pp. 167-198
Publisher:Springer
ISSN:1869-2672
Status:Published
Keywords:Greedy algorithm, Inverse gravimetry, Nonlinear inverse problem, Regularization
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Technik für Raumfahrtsysteme
DLR - Research theme (Project):R - Vorhaben SISTEC
Location: Köln-Porz
Institutes and Institutions:Institut of Simulation and Software Technology > High Performance Computing
Deposited By: Kontak, Max
Deposited On:26 Nov 2018 14:21
Last Modified:14 Dec 2019 04:25

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