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Dissertations / Theses on the topic 'Tikhonov regularization method'

Author: Grafiati

Published: 4 June 2021

Last updated: 27 July 2025

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1

Whitney, MaryGeorge L. "Theoretical and Numerical Study of Tikhonov's Regularization and Morozov's Discrepancy Principle." Digital Archive @ GSU, 2009. http://digitalarchive.gsu.edu/math_theses/77.

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A concept of a well-posed problem was initially introduced by J. Hadamard in 1923, who expressed the idea that every mathematical model should have a unique solution, stable with respect to noise in the input data. If at least one of those properties is violated, the problem is ill-posed (and unstable). There are numerous examples of ill- posed problems in computational mathematics and applications. Classical numerical algorithms, when used for an ill-posed model, turn out to be divergent. Hence one has to develop special regularization techniques, which take advantage of an a priori informati

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2

Yu, Xuebo. "Generalized Krylov subspace methods with applications." Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1401937618.

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3

Oliveira, Claudir. "Implementação paralela do algoritmo iterativo de busca do parâmetro de regularização ótimo para o funcional de Tikhonov no problema de restauração de imagens." Universidade do Estado do Rio de Janeiro, 2012. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=4513.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>O uso de técnicas com o funcional de Tikhonov em processamento de imagens tem sido amplamente usado nos últimos anos. A ideia básica nesse processo é modificar uma imagem inicial via equação de convolução e encontrar um parâmetro que minimize esse funcional afim de obter uma aproximação da imagem original. Porém, um problema típico neste método consiste na seleção do parâmetro de regularização adequado para o compromisso entre a acurácia e a estabilidade da solução. Um método desenvolvido por pesquisadores do IPRJ e UFRJ, atuantes

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4

Kříž, Tomáš. "Nové typy a principy optimalizace digitálního zpracování obrazů v EIT." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-234654.

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This doctoral thesis proposes a new algorithm for the reconstruction of impedance images in monitored objects. The algorithm eliminates the spatial resolution problems present in existing reconstruction methods, and, with respect to the monitored objects, it exploits both the partial knowledge of configuration and the material composition. The discussed novel method is designed to recognize certain significant fields of interest, such as material defects or blood clots and tumors in biological images. The actual reconstruction process comprises two phases; while the former stage is focused on

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5

Abbas, Boushra. "Méthode de Newton régularisée pour les inclusions monotones structurées : étude des dynamiques et algorithmes associés." Thesis, Montpellier, 2015. http://www.theses.fr/2015MONTS250/document.

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Cette thèse est consacrée à la recherche des zéros d'un opérateur maximal monotone structuré, à l'aide de systèmes dynamiques dissipatifs continus et discrets. Les solutions sont obtenues comme limites des trajectoires lorsque le temps t tend vers l'infini. On s'intéressera principalement aux dynamiques obtenues par régularisation de type Levenberg-Marquardt de la méthode de Newton. On décrira aussi les approches basées sur des dynamiques voisines.Dans un cadre Hilbertien, on s'intéresse à la recherche des zéros de l'opérateur maximal monotone structuré M = A + B, où A est un opérateur maximal

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6

Kořínková, Ksenia. "Vylepšení metodiky rekonstrukce biomedicínských obrazů založené na impedanční tomografii." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-256564.

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Disertační práce, jež má teoretický charakter, je zaměřena na vylepšení a výzkum algoritmů pro zobrazování vnitřní struktury vodivých objektů, hlavně biologických tkání a orgánů pomocí elektrické impedanční tomografie (EIT). V práci je formulován teoretický rámec EIT. Dále jsou prezentovány a porovnány algoritmy pro řešení inverzní úlohy, které zajišťují efektivní rekonstrukci prostorového rozložení elektrických vlastností ve zkoumaném objektu a jejích zobrazení. Hlavní myšlenka vylepšeného algoritmu, který je založen na deterministickém přístupu, spočívá v zavedení dodatečných technik: level

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7

Hans, Esther [Verfasser]. "Globally convergent B-semismooth Newton methods for l1-Tikhonov regularization / Esther Hans." Mainz : Universitätsbibliothek Mainz, 2017. http://d-nb.info/1131905032/34.

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8

Azpiroz, Izar. "Contribution à la Résolution Numérique de Problèmes Inverses de Diffraction Élasto-acoustique." Thesis, Pau, 2018. http://www.theses.fr/2018PAUU3004/document.

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La caractérisation d’objets enfouis à partir de mesures d’ondes diffractées est un problème présent dans de nombreuses applications comme l’exploration géophysique, le contrôle non-destructif, l’imagerie médicale, etc. Elle peut être obtenue numériquement par la résolution d’un problème inverse. Néanmoins, c’est un problème non linéaire et mal posé, ce qui rend la tâche difficile. Une reconstruction précise nécessite un choix judicieux de plusieurs paramètres très différents, dépendant des données de la méthode numérique d’optimisation choisie.La contribution principale de cette thèse est une

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9

Rückert, Nadja. "Studies on two specific inverse problems from imaging and finance." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-91587.

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This thesis deals with regularization parameter selection methods in the context of Tikhonov-type regularization with Poisson distributed data, in particular the reconstruction of images, as well as with the identiﬁcation of the volatility surface from observed option prices. In Part I we examine the choice of the regularization parameter when reconstructing an image, which is disturbed by Poisson noise, with Tikhonov-type regularization. This type of regularization is a generalization of the classical Tikhonov regularization in the Banach space setting and often called variational regulariza

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10

Slagel, Joseph Tanner. "Row-Action Methods for Massive Inverse Problems." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90377.

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Numerous scientific applications have seen the rise of massive inverse problems, where there are too much data to implement an all-at-once strategy to compute a solution. Additionally, tools for regularizing ill-posed inverse problems are infeasible when the problem is too large. This thesis focuses on the development of row-action methods, which can be used to iteratively solve inverse problems when it is not possible to access the entire data-set or forward model simultaneously. We investigate these techniques for linear inverse problems and for separable, nonlinear inverse problems where th

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11

Gazzola, Silvia. "Regularization techniques based on Krylov subspace methods for ill-posed linear systems." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3423528.

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This thesis is focussed on the regularization of large-scale linear discrete ill-posed problems. Problems of this kind arise in a variety of applications, and, in a continuous setting, they are often formulated as Fredholm integral equations of the first kind, with smooth kernel, modeling an inverse problem (i.e., the unknown of these equations is the cause of an observed effect). Upon discretization, linear systems whose coefficient matrix is ill-conditioned and whose right-hand side vector is affected by some perturbations (noise) must be solved. %Because of the ill-conditioning of the syste

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12

Kayhan, Belgin. "Parameter Estimation In Generalized Partial Linear Modelswith Tikhanov Regularization." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612530/index.pdf.

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Regression analysis refers to techniques for modeling and analyzing several variables in statistical learning. There are various types of regression models. In our study, we analyzed Generalized Partial Linear Models (GPLMs), which decomposes input variables into two sets, and additively combines classical linear models with nonlinear model part. By separating linear models from nonlinear ones, an inverse problem method Tikhonov regularization was applied for the nonlinear submodels separately, within the entire GPLM. Such a particular representation of submodels provides both a better accurac

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13

Shao, Yuanyuan. "Beiträge zur Regularisierung inverser Probleme und zur bedingten Stabilität bei partiellen Differentialgleichungen." Doctoral thesis, Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-102801.

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Wir betrachten die lineare inverse Probleme mit gestörter rechter Seite und gestörtem Operator in Hilberträumen, die inkorrekt sind. Um die Auswirkung der Inkorrektheit zu verringen, müssen spezielle Lösungsmethode angewendet werden, hier nutzen wir die sogenannte Tikhonov Regularisierungsmethode. Die Regularisierungsparameter wählen wir aus das verallgemeinerte Defektprinzip. Eine typische numerische Methode zur Lösen der nichtlinearen äquivalenten Defektgleichung ist Newtonverfahren. Wir schreiben einen Algorithmus, die global und monoton konvergent für beliebige Startwerte garantiert. Um

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14

Pasha, Mirjeta. "Krylov subspace type methods for the computation of non-negative or sparse solutions of ill-posed problems." Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1586459362313778.

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15

Hamilton, Lei Hou. "Reduced-data magnetic resonance imaging reconstruction methods: constraints and solutions." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42707.

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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

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16

Cho, Taewon. "Computational Advancements for Solving Large-scale Inverse Problems." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/103772.

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For many scientific applications, inverse problems have played a key role in solving important problems by enabling researchers to estimate desired parameters of a system from observed measurements. For example, large-scale inverse problems arise in many global problems and medical imaging problems such as greenhouse gas tracking and computational tomography reconstruction. This dissertation describes advancements in computational tools for solving large-scale inverse problems and for uncertainty quantification. Oftentimes, inverse problems are ill-posed and large-scale. Iterative projection m

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17

Estecahandy, Elodie. "Contribution à l'analyse mathématique et à la résolution numérique d'un problème inverse de scattering élasto-acoustique." Phd thesis, Université de Pau et des Pays de l'Adour, 2013. http://tel.archives-ouvertes.fr/tel-00880628.

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La détermination de la forme d'un obstacle élastique immergé dans un milieu fluide à partir de mesures du champ d'onde diffracté est un problème d'un vif intérêt dans de nombreux domaines tels que le sonar, l'exploration géophysique et l'imagerie médicale. A cause de son caractère non-linéaire et mal posé, ce problème inverse de l'obstacle (IOP) est très difficile à résoudre, particulièrement d'un point de vue numérique. De plus, son étude requiert la compréhension de la théorie du problème de diffraction direct (DP) associé, et la maîtrise des méthodes de résolution correspondantes. Le travai

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18

UGWU, UGOCHUKWU OBINNA. "Iterative tensor factorization based on Krylov subspace-type methods with applications to image processing." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1633531487559183.

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19

GAZZOLA, SILVIA. "Regularization techniques based on Krylov subspace methods for ill-posed linear systems." Doctoral thesis, 2014. http://hdl.handle.net/11577/3040700.

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Questa tesi è incentrata sulle tecniche di regolarizzazione per problemi lineari discreti malposti e di grandi dimensioni. Molteplici applicazioni fisiche ed ingegneristiche sono modellate da questo genere di problemi che, in ambito continuo, sono spesso formulati mediante equazioni integrali di Fredholm di prima specie con nucleo regolare. Più precisamente, queste equazioni modellano i cosiddetti problemi inversi, cioè problemi in cui la causa di un effetto osservato deve essere ricostruita. Una volta discretizzati, questi problemi si presentano come sistemi lineari, la cui matrice dei coeffi

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20

Gupta, Hari Shanker. "Numerical Study Of Regularization Methods For Elliptic Cauchy Problems." Thesis, 2010. https://etd.iisc.ac.in/handle/2005/1249.

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Cauchy problems for elliptic partial differential equations arise in many important applications, such as, cardiography, nondestructive testing, heat transfer, sonic boom produced by a maneuvering aerofoil, etc. Elliptic Cauchy problems are typically ill-posed, i.e., there may not be a solution for some Cauchy data, and even if a solution exists uniquely, it may not depend continuously on the Cauchy data. The ill-posedness causes numerical instability and makes the classical numerical methods inappropriate to solve such problems. For Cauchy problems, the research on uniqueness, stability, and

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21

Gupta, Hari Shanker. "Numerical Study Of Regularization Methods For Elliptic Cauchy Problems." Thesis, 2010. http://etd.iisc.ernet.in/handle/2005/1249.

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Cauchy problems for elliptic partial differential equations arise in many important applications, such as, cardiography, nondestructive testing, heat transfer, sonic boom produced by a maneuvering aerofoil, etc. Elliptic Cauchy problems are typically ill-posed, i.e., there may not be a solution for some Cauchy data, and even if a solution exists uniquely, it may not depend continuously on the Cauchy data. The ill-posedness causes numerical instability and makes the classical numerical methods inappropriate to solve such problems. For Cauchy problems, the research on uniqueness, stability, and

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22

Eckhardt, Julian. "Bending energy regularization on shape spaces: a class of iterative methods on manifolds and applications to inverse obstacle problems." Doctoral thesis, 2019. http://hdl.handle.net/21.11130/00-1735-0000-0005-12D0-B.

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23

Shao, Yuanyuan. "Beiträge zur Regularisierung inverser Probleme und zur bedingten Stabilität bei partiellen Differentialgleichungen." Doctoral thesis, 2012. https://monarch.qucosa.de/id/qucosa%3A19827.

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Abstract:

Wir betrachten die lineare inverse Probleme mit gestörter rechter Seite und gestörtem Operator in Hilberträumen, die inkorrekt sind. Um die Auswirkung der Inkorrektheit zu verringen, müssen spezielle Lösungsmethode angewendet werden, hier nutzen wir die sogenannte Tikhonov Regularisierungsmethode. Die Regularisierungsparameter wählen wir aus das verallgemeinerte Defektprinzip. Eine typische numerische Methode zur Lösen der nichtlinearen äquivalenten Defektgleichung ist Newtonverfahren. Wir schreiben einen Algorithmus, die global und monoton konvergent für beliebige Startwerte garantiert. Um

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