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Title
Higher order regularization for model based data decompression / vorgelegt von Martin Holler
Additional Titles
Higher order regularization for model based data decompression
AuthorHoller, Martin
CensorKunisch Karl ; Andreas Neubauer
Published2013
Description155 S. : 2 Zsfassungen ; Ill., graph. Darst.
Institutional NoteGraz, Univ., Diss., 2013
Annotation
Abweichender Titel laut Übersetzung der Verfasserin/des Verfassers
Zsfassung in dt. und engl. Sprache
LanguageGerman
Bibl. ReferenceOeBB
Document typeDissertation (PhD)
Keywords (GND)Bildrekonstruktion / Mathematisches Modell / Bildrekonstruktion / Mathematisches Modell / Online-Publikation
URNurn:nbn:at:at-ubg:1-46893 Persistent Identifier (URN)
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 The work is publicly available
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Higher order regularization for model based data decompression [6.95 mb]
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Abstract (German)

Diese Doktorarbeit befasst sich mit der Entwicklung, Analyse und Anwendung eines mathematischen Modells zur Bildrekonstruktion. Das Modell wird durch die Minimierung der Summe zweier konvexer Funktionale realisiert. Eines dieser Funktionale stellt die Datentreue sicher während das andere zur Regularisierung dient. Neu an dem hier vorgestellten Zugang ist sowohl die allgemeine Formulierungdes Datenterms als auch die Anwendung des emph

Abstract (English)

This thesis deals with the development, analysis and application of a mathematical model for image reconstruction. The model is realized by minimizing the sum of two convex functionals, one ensuring data fidelity and the other being a regularization term. The novelty of the considered approach lies both in the general definition of the data term as well as the application of the non-standard Total Generalized Variation (TGV) functional for regularization in this context. The main part of the work is the extension of theory for the TGV functional, the definition and analysis of the general reconstruction model and its application to imaging tasks. In particular, existence of a solution and optimality conditions for the resulting minimization problem are obtained for a setting that covers diverse applications: Suitable problem formulations for JPEG and JPEG 2000 decompression as well as wavelet based zooming are defined in function space setting and numerical solution schemes for the discretized problems are developed.

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