Skip navigation
SuUB logo
DSpace logo

  • Home
  • Institutions
    • University of Bremen
    • City University of Applied Sciences
    • Bremerhaven University of Applied Sciences
  • Sign on to:
    • My Media
    • Receive email
      updates
    • Edit Account details

Citation link: http://nbn-resolving.de/urn:nbn:de:gbv:46-diss000112632
00011263.pdf
OpenAccess
 
copyright

Adaptive Frame Based Regularization Methods for Linear Ill-Posed Inverse Problems.


File Description SizeFormat
00011263.pdf1.16 MBAdobe PDFView/Open
Other Titles: Adaptive Framebasierte Regularisierungsmethoden für Lineare Schlechtgestellte Inverse Probleme.
Authors: Zhariy, Mariya 
Supervisor: Teschke, Gerd
1. Expert: Teschke, Gerd
2. Expert: Maass, Peter  
Abstract: 
This thesis is concerned with the development and analysis of adaptiveregularization methods for solving linear inverse ill-posed problems.Based on nonlinear approximation theory, the adaptivity concept has becomepopular in the field of well-posed problems, especially in the solution of elliptic PDE's.Under certain conditions on the smoothness of the solution and the compressibility of the operatorit has been shown that the nonlinear approximation guarantees a more efficient approximationwith respect to the sparsity of the solution and to the computational effort.In the area of inverse problems, the sparse approximation approachhas been applied in solving de-noising and de-blurring problems as well as in general regularization.An essential cost reduction has been achieved by newlydeveloped strategies like domain decomposition and specific projection methods.However, the option of adaptive application, leading simultaneously to cost reduction and sparse approximation,has not been taken into account yet.In our research we combine the advantages of the nonlinear approximation with theclassical regularization and parameter identification strategies, like Tikhonov and Landwebermethods. We modify the classical approach for solving the ill-posed inverse problemsin order to obtain a sparse approximation with essentially reduced numerical effort.The main novelty of the developed regularization methods is the adaptive operator approximation.In general, we have shown that it is possible to construct adaptive regularization methods,which yield the same convergence rates as the conventional regularization methods, but aremuch more efficient with respect to the numerical costs.The analytic results of this work have been confirmed and complemented by numerical experiments,that illustrate the sparsity of the obtained solution and desired convergence rates.
Keywords: Nonlinear Approximation, Wavelets, Adaptivity, Linear Inverse Problems, Adaptive Regularization, Best N-Term Approximation, Compressive Methods, Adaptive Grid, Tomographic Reconstruction
Issue Date: 12-Jan-2009
Type: Dissertation
URN: urn:nbn:de:gbv:46-diss000112632
Institution: Universität Bremen 
Faculty: FB3 Mathematik/Informatik 
Appears in Collections:Dissertationen

  

Page view(s)

24
checked on Jan 19, 2021

Download(s)

2
checked on Jan 19, 2021

Google ScholarTM

Check


Items in Media are protected by copyright, with all rights reserved, unless otherwise indicated.

Legal notice -Feedback -Data privacy
Media - Extension maintained and optimized by Logo 4SCIENCE