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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
21

Contributions to regularization theory and practice of certain nonlinear inverse problems

Hofmann, Christopher 23 December 2020 (has links)
The present thesis addresses both theoretical as well as numerical aspects of the treatment of nonlinear inverse problems. The first part considers Tikhonov regularization for nonlinear ill-posed operator equations in Hilbert scales with oversmoothing penalties. Sufficient as well as necessary conditions to establish convergence are introduced and convergence rate results are given for various parameter choice rules under a two sided nonlinearity constraint. Ultimately, both a posteriori as well as certain a priori parameter choice rules lead to identical converce rates. The theoretical results are supported and augmented by extensive numerical case studies. In particular it is shown, that the localization of the above mentioned nonlinearity constraint is not trivial. Incorrect localization will prevent convergence of the regularized to the exact solution. The second part of the thesis considers two open problems in inverse option pricing and electrical impedance tomography. While regularization through discretization is sufficient to overcome ill-posedness of the latter, the first requires a more sophisticated approach. It is shown, that the recovery of time dependent volatility and interest rate functions from observed option prices is everywhere locally ill-posed. This motivates Tikhonov-type or variational regularization with two parameters and penalty terms to simultaneously recover these functions. Two parameter choice rules using the L-hypersurface as well as a combination of L-curve and quasi-optimality are introduced. The results are again supported by extensive numerical case studies.
22

Bending energy regularization on shape spaces: a class of iterative methods on manifolds and applications to inverse obstacle problems

Eckhardt, Julian 11 September 2019 (has links)
No description available.
23

Maximum entropy regularization for calibrating a time-dependent volatility function

Hofmann, Bernd, Krämer, Romy 26 August 2004 (has links)
We investigate the applicability of the method of maximum entropy regularization (MER) including convergence and convergence rates of regularized solutions to the specific inverse problem (SIP) of calibrating a purely time-dependent volatility function. In this context, we extend the results of [16] and [17] in some details. Due to the explicit structure of the forward operator based on a generalized Black-Scholes formula the ill-posedness character of the nonlinear inverse problem (SIP) can be verified. Numerical case studies illustrate the chances and limitations of (MER) versus Tikhonov regularization (TR) for smooth solutions and solutions with a sharp peak.
24

Generalized Krylov subspace methods with applications

Yu, Xuebo 07 August 2014 (has links)
No description available.
25

Restauração de imagens de microscopia de força atômica com uso da regularização de Tikhonov via processamento em GPU / Image restoration from atomic force microscopy using the Tikhonov regularization via GPU processing

Augusto Garcia Almeida 04 March 2013 (has links)
A Restauração de Imagens é uma técnica que possui aplicações em várias áreas, por exemplo, medicina, biologia, eletrônica, e outras, onde um dos objetivos da restauração de imagens é melhorar o aspecto final de imagens de amostras que por algum motivo apresentam imperfeições ou borramentos. As imagens obtidas pelo Microscópio de Força Atômica apresentam borramentos causados pela interação de forças entre a ponteira do microscópio e a amostra em estudo. Além disso apresentam ruídos aditivos causados pelo ambiente. Neste trabalho é proposta uma forma de paralelização em GPU de um algoritmo de natureza serial que tem por fim a Restauração de Imagens de Microscopia de Força Atômica baseado na Regularização de Tikhonov. / Image Restoration is a technique which has applications in several areas, e.g., medicine, biology, electronics, and others, where one of the goals is to improve the final appearance of the images of samples, that have for some reason, imperfections or blurring. The images obtained by Atomic Force Microscope have blurring caused by the interaction forces between the tip of the microscope and the sample under study. Moreover exhibit additive noise caused by the environment. This thesis proposes a way to make a parallelization on a GPU of a serial algorithm of which is a Image Restoration of Images from Atomic Force Microscopy using Tikhonov Regularization.
26

Reduced-data magnetic resonance imaging reconstruction methods: constraints and solutions.

Hamilton, Lei Hou 11 August 2011 (has links)
Imaging speed is very important in magnetic resonance imaging (MRI), especially in dynamic cardiac applications, which involve respiratory motion and heart motion. With the introduction of reduced-data MR imaging methods, increasing acquisition speed has become possible without requiring a higher gradient system. But these reduced-data imaging methods carry a price for higher imaging speed. This may be a signal-to-noise ratio (SNR) penalty, reduced resolution, or a combination of both. Many methods sacrifice edge information in favor of SNR gain, which is not preferable for applications which require accurate detection of myocardial boundaries. The central goal of this thesis is to develop novel reduced-data imaging methods to improve reconstructed image performance. This thesis presents a novel reduced-data imaging method, PINOT (Parallel Imaging and NOquist in Tandem), to accelerate MR imaging. As illustrated by a variety of computer simulated and real cardiac MRI data experiments, PINOT preserves the edge details, with flexibility of improving SNR by regularization. Another contribution is to exploit the data redundancy from parallel imaging, rFOV and partial Fourier methods. A Gerchberg Reduced Iterative System (GRIS), implemented with the Gerchberg-Papoulis (GP) iterative algorithm is introduced. Under the GRIS, which utilizes a temporal band-limitation constraint in the image reconstruction, a variant of Noquist called iterative implementation iNoquist (iterative Noquist) is proposed. Utilizing a different source of prior information, first combining iNoquist and Partial Fourier technique (phase-constrained iNoquist) and further integrating with parallel imaging methods (PINOT-GRIS) are presented to achieve additional acceleration gains.
27

Generalized Tikhonov regularization

Flemming, Jens 01 November 2011 (has links) (PDF)
The dissertation suggests a generalized version of Tikhonov regularization and analyzes its properties. The focus is on convergence rates theory and an extensive example for regularization with Poisson distributed data is given.
28

Restauração de imagens de microscopia de força atômica com uso da regularização de Tikhonov via processamento em GPU / Image restoration from atomic force microscopy using the Tikhonov regularization via GPU processing

Augusto Garcia Almeida 04 March 2013 (has links)
A Restauração de Imagens é uma técnica que possui aplicações em várias áreas, por exemplo, medicina, biologia, eletrônica, e outras, onde um dos objetivos da restauração de imagens é melhorar o aspecto final de imagens de amostras que por algum motivo apresentam imperfeições ou borramentos. As imagens obtidas pelo Microscópio de Força Atômica apresentam borramentos causados pela interação de forças entre a ponteira do microscópio e a amostra em estudo. Além disso apresentam ruídos aditivos causados pelo ambiente. Neste trabalho é proposta uma forma de paralelização em GPU de um algoritmo de natureza serial que tem por fim a Restauração de Imagens de Microscopia de Força Atômica baseado na Regularização de Tikhonov. / Image Restoration is a technique which has applications in several areas, e.g., medicine, biology, electronics, and others, where one of the goals is to improve the final appearance of the images of samples, that have for some reason, imperfections or blurring. The images obtained by Atomic Force Microscope have blurring caused by the interaction forces between the tip of the microscope and the sample under study. Moreover exhibit additive noise caused by the environment. This thesis proposes a way to make a parallelization on a GPU of a serial algorithm of which is a Image Restoration of Images from Atomic Force Microscopy using Tikhonov Regularization.
29

Convergence rates for variational regularization of statistical inverse problems

Sprung, Benjamin 04 October 2019 (has links)
No description available.
30

Generalized Tikhonov regularization: Basic theory and comprehensive results on convergence rates

Flemming, Jens 27 October 2011 (has links)
The dissertation suggests a generalized version of Tikhonov regularization and analyzes its properties. The focus is on convergence rates theory and an extensive example for regularization with Poisson distributed data is given.

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