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  4. Regularization Methods in Banach Spaces applied to Inverse Medium Scattering Problems
 
Zitierlink URN
https://nbn-resolving.de/urn:nbn:de:gbv:46-00105983-18

Regularization Methods in Banach Spaces applied to Inverse Medium Scattering Problems

Veröffentlichungsdatum
2017-06-26
Autoren
Rennoch, Marcel  
Betreuer
Lechleiter, Armin  
Gutachter
King, Emily  
Zusammenfassung
This work handles inverse scattering problems for both acoustic and electromagnetic waves. That is to reconstruct the irradiated media from measurements of the scattered felds by regularization methods. As a particular feature, the contrasts of the scattering objects are assumed to be supported within a small region, hence called sparse. To apply sparsity regularization schemes it becomes crucial to model the problems in Banach spaces. Traditionally, they are given in a Hilbert space setting, such that reformulation in an L p-sense becomes a key point. Contrasts are linked to the data by forward operators, basing on beforehand stated solution operators and their continuity properties. Thereby, appropriate regularization techniques providing sparsity are given. As the case of scalar-valued contrast functions is already covered in the literature, mainly inverse scattering problems for anisotropic media are shown. In the case where electromagnetic waves are considered, a distinction is made between magnetic and non-magnetic media, since the latter is less complex. Finally, the case of inverse acoustic backscattering is handled, which is rarely seen in literature.
Schlagwörter
inverse scattering problems

; 

sparsity

; 

regularization theory

; 

Tikhonov regularization methods

; 

anisotropic media

; 

backscattering
Institution
Universität Bremen  
Fachbereich
Fachbereich 03: Mathematik/Informatik (FB 03)  
Dokumenttyp
Dissertation
Zweitveröffentlichung
Nein
Sprache
Englisch
Dateien
Lade...
Vorschaubild
Name

00105983-1.pdf

Size

1.74 MB

Format

Adobe PDF

Checksum

(MD5):a2f4a11f98932a9fc29b9bc4c968449d

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