Adaptive spectral decompositions for inverse medium problems

Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all too often computationally prohibitive due to the high dimens...

Full description

Saved in:
Bibliographic Details
Main Authors Baffet, Daniel H, Grote, Marcus J, Tang, Jet Hoe
Format Journal Article
LanguageEnglish
Published 17.06.2020
Subjects
Online AccessGet full text

Cover

Loading…
Abstract Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all too often computationally prohibitive due to the high dimension of the search space. Adaptive spectral (AS) decompositions instead expand the unknown medium in a basis of eigenfunctions of a judicious elliptic operator, which depends itself on the medium. Here the AS decomposition is combined with a standard inexact Newton-type method for the solution of time-harmonic scattering problems governed by the Helmholtz equation. By repeatedly adapting both the eigenfunction basis and its dimension, the resulting adaptive spectral inversion (ASI) method substantially reduces the dimension of the search space during the nonlinear optimization. Rigorous estimates of the AS decomposition are proved for a general piecewise constant medium. Numerical results illustrate the accuracy and efficiency of the ASI method for time-harmonic inverse scattering problems, including a salt dome model from geophysics.
AbstractList Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all too often computationally prohibitive due to the high dimension of the search space. Adaptive spectral (AS) decompositions instead expand the unknown medium in a basis of eigenfunctions of a judicious elliptic operator, which depends itself on the medium. Here the AS decomposition is combined with a standard inexact Newton-type method for the solution of time-harmonic scattering problems governed by the Helmholtz equation. By repeatedly adapting both the eigenfunction basis and its dimension, the resulting adaptive spectral inversion (ASI) method substantially reduces the dimension of the search space during the nonlinear optimization. Rigorous estimates of the AS decomposition are proved for a general piecewise constant medium. Numerical results illustrate the accuracy and efficiency of the ASI method for time-harmonic inverse scattering problems, including a salt dome model from geophysics.
Author Grote, Marcus J
Tang, Jet Hoe
Baffet, Daniel H
Author_xml – sequence: 1
  givenname: Daniel H
  surname: Baffet
  fullname: Baffet, Daniel H
– sequence: 2
  givenname: Marcus J
  surname: Grote
  fullname: Grote, Marcus J
– sequence: 3
  givenname: Jet Hoe
  surname: Tang
  fullname: Tang, Jet Hoe
BackLink https://doi.org/10.48550/arXiv.2006.09682$$DView paper in arXiv
BookMark eNotj71uwyAYABnaoU37AJ3KC9jFYAOWskRR_6RIXbJbGL5PQjIGgWO1b5807XTb6e6e3MxxBkKeGla3uuvYi8nffq05Y7JmvdT8jmx3zqTFr0BLArtkM1EHNoYUi198nAvFmKmfV8gFaADnT4GmHMcJQnkgt2imAo__3JDj2-tx_1Edvt4_97tDZaTiFbrG9CPyRmgG2mqhlOmYA9OgBhzVJcQpJVGJsbWAXFjeIkouOiF77pTYkOc_7TV_SNkHk3-G343huiHOGlJFNg
ContentType Journal Article
Copyright http://arxiv.org/licenses/nonexclusive-distrib/1.0
Copyright_xml – notice: http://arxiv.org/licenses/nonexclusive-distrib/1.0
DBID AKY
AKZ
GOX
DOI 10.48550/arxiv.2006.09682
DatabaseName arXiv Computer Science
arXiv Mathematics
arXiv.org
DatabaseTitleList
Database_xml – sequence: 1
  dbid: GOX
  name: arXiv.org
  url: http://arxiv.org/find
  sourceTypes: Open Access Repository
DeliveryMethod fulltext_linktorsrc
ExternalDocumentID 2006_09682
GroupedDBID AKY
AKZ
GOX
ID FETCH-LOGICAL-a672-fd1a9bf21380e8c8377a50dea1f8efb7968d776f73b4cef23c24ff62353692d73
IEDL.DBID GOX
IngestDate Mon Jan 08 05:43:14 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-a672-fd1a9bf21380e8c8377a50dea1f8efb7968d776f73b4cef23c24ff62353692d73
OpenAccessLink https://arxiv.org/abs/2006.09682
ParticipantIDs arxiv_primary_2006_09682
PublicationCentury 2000
PublicationDate 2020-06-17
PublicationDateYYYYMMDD 2020-06-17
PublicationDate_xml – month: 06
  year: 2020
  text: 2020-06-17
  day: 17
PublicationDecade 2020
PublicationYear 2020
Score 1.7759018
SecondaryResourceType preprint
Snippet Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of...
SourceID arxiv
SourceType Open Access Repository
SubjectTerms Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
Mathematics - Optimization and Control
Title Adaptive spectral decompositions for inverse medium problems
URI https://arxiv.org/abs/2006.09682
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV07SwNBEF5iKhtRVOKTLWwPc_s-sAliDILaRLgu7N7sQApDuCTiz3d274I2trtT7APmm2G-mY-xO5_6MbWWhYGSEhRCoCKACoUKVSJFaQVZkuX1zcw-1Eut6wHj-14Y334vv7r5wGFz39UKKuPIyR4IkShbz-91V5zMo7h6-187ijHz0h-QmB6zoz6645PuO07YIK5O2cME_Dp5FZ7bGlsygJio3Hu-FKfAkS9XiSAReSp27z55L_SyOWPz6dP8cVb0ogWFN1YUCKWvAopSunF0DaV_1usxRF-iixgsnRGsNWhlUE1EIRuhECkG0dJUAqw8Z0PK--OIcSEjemEBnZOEo9FHoRtQaIKEyqK-YKN81cW6m0uRFCXNIr_C5f9bV-xQpJQxye_Yazbctrt4Q7i6Dbf5cX8A_2Z4jA
link.rule.ids 228,230,786,891
linkProvider Cornell University
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Adaptive+spectral+decompositions+for+inverse+medium+problems&rft.au=Baffet%2C+Daniel+H&rft.au=Grote%2C+Marcus+J&rft.au=Tang%2C+Jet+Hoe&rft.date=2020-06-17&rft_id=info:doi/10.48550%2Farxiv.2006.09682&rft.externalDocID=2006_09682