Relevant bibliographies by topics / Tikhonov-Regularisierung

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Academic literature on the topic 'Tikhonov-Regularisierung'

Author: Grafiati
Published: 4 June 2021
Last updated: 19 February 2022

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Dissertations / Theses on the topic "Tikhonov-Regularisierung"

1

Gerth, Daniel. "Tikhonov regularization with oversmoothing penalties." Universitätsbibliothek Chemnitz, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-216262.

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In the last decade l1-regularization became a powerful and popular tool for the regularization of Inverse Problems. While in the early years sparse solution were in the focus of research, recently also the case that the coefficients of the exact solution decay sufficiently fast was under consideration. In this paper we seek to show that l1-regularization is applicable and leads to optimal convergence rates even when the exact solution does not belong to l1 but only to l2. This is a particular example of over-smoothing regularization, i.e., the penalty implies smoothness properties the exact s
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Flemming, Jens. "Generalized Tikhonov regularization." Doctoral thesis, Universitätsbibliothek Chemnitz, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-78152.

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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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Anzengruber, Stephan W., Bernd Hofmann, and Peter Mathé. "Regularization properties of the discrepancy principle for Tikhonov regularization in Banach spaces." Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-99353.

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The stable solution of ill-posed non-linear operator equations in Banach space requires regularization. One important approach is based on Tikhonov regularization, in which case a one-parameter family of regularized solutions is obtained. It is crucial to choose the parameter appropriately. Here, a variant of the discrepancy principle is analyzed. In many cases such parameter choice exhibits the feature, called regularization property below, that the chosen parameter tends to zero as the noise tends to zero, but slower than the noise level. Here we shall show such regularization property under
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4

Bürger, Steven, and Bernd Hofmann. "About a deficit in low order convergence rates on the example of autoconvolution." Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-130630.

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We revisit in L2-spaces the autoconvolution equation x ∗ x = y with solutions which are real-valued or complex-valued functions x(t) defined on a finite real interval, say t ∈ [0,1]. Such operator equations of quadratic type occur in physics of spectra, in optics and in stochastics, often as part of a more complex task. Because of their weak nonlinearity deautoconvolution problems are not seen as difficult and hence little attention is paid to them wrongly. In this paper, we will indicate on the example of autoconvolution a deficit in low order convergence rates for regularized solutions of no
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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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Bot, Radu Ioan, and Bernd Hofmann. "The impact of a curious type of smoothness conditions on convergence rates in l1-regularization." Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-104381.

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Tikhonov-type regularization of linear and nonlinear ill-posed problems in abstract spaces under sparsity constraints gained relevant attention in the past years. Since under some weak assumptions all regularized solutions are sparse if the l1-norm is used as penalty term, the l1-regularization was studied by numerous authors although the non-reflexivity of the Banach space l1 and the fact that such penalty functional is not strictly convex lead to serious difficulties. We consider the case that the sparsity assumption is narrowly missed. This means that the solutions may have an infinite numb
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Motta-Ribeiro, Gabriel Casulari, Frederico Caetano Jandre, Hermann Wrigge, and Antonio Giannella-Neto. "Generalized estimation of the ventilatory distribution from the multiple‑breath nitrogen washout." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-208275.

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Background: This work presents a generalized technique to estimate pulmonary ventilation-to-volume (v/V) distributions using the multiple-breath nitrogen washout, in which both tidal volume (VT) and the end-expiratory lung volume (EELV) are allowed to vary during the maneuver. In addition, the volume of the series dead space (vd), unlike the classical model, is considered a common series unit connected to a set of parallel alveolar units. Methods: The numerical solution for simulated data, either error-free or with the N2 measurement contaminated with the addition of Gaussian random noise of 3
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8

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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9

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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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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Book chapters on the topic "Tikhonov-Regularisierung"

1

Rieder, Andreas. "Tikhonov—Phillips-Regularisierung." In Keine Probleme mit Inversen Problemen. Vieweg+Teubner Verlag, 2003. http://dx.doi.org/10.1007/978-3-322-80234-7_4.

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Hastenteufel, Mark, Ivo Wolf, Sibylle Mottl-Link, Raffaele de Simone, and Hans-Peter Meinzer. "Rekonstruktion von Myokardgeschwindigkeiten mittels Tikhonov Regularisierung." In Informatik aktuell. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-18993-7_25.

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