Relevant bibliographies by topics / Tikhonov regularization method

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Tikhonov regularization method'

Author: Grafiati
Published: 4 June 2021
Last updated: 27 July 2025

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Journal articles on the topic "Tikhonov regularization method"

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Sjöberg, L. "Solutions to Linear Inverse Problems on the Sphere by Tikhonov Regularization, Wiener filtering and Spectral Smoothing and Combination — A Comparison." Journal of Geodetic Science 2, no. 1 (2012): 31–37. http://dx.doi.org/10.2478/v10156-011-0021-z.

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Solutions to Linear Inverse Problems on the Sphere by Tikhonov Regularization, Wiener filtering and Spectral Smoothing and Combination — A ComparisonSolutions to linear inverse problems on the sphere, common in geodesy and geophysics, are compared for Tikhonov's method of regularization, Wiener filtering and spectral smoothing and combination as well as harmonic analysis. It is concluded that Wiener and spectral smoothing, although based on different assumptions and target functions, yield the same estimator. Also, provided that the extra information on the signal and error degree variances is
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Zeng, Xiaoniu, Tianyou Liu, Xiaofeng Tan, Hongru Li, and Shengjie Luo. "An improved Tikhonov regularization method combined with the exponential filter function." Journal of Computational Methods in Sciences and Engineering 25, no. 2 (2024): 1114–22. https://doi.org/10.1177/14727978241295283.

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Tikhonov regularization is one of the most popular methods for solving linear discrete ill-posed problems. This approach involves transforming the original problem into a penalized least-squares problem, yielding a solution that exhibits greater robustness against data inaccuracies and computational errors that may occur during the solving process. The choice of the regularization matrix significantly influences the accuracy of the resulting solution. In this paper, we propose a novel method for selecting the regularization matrix based on exponential filter functions, which have a unique conn
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Al-Mahdawi, H. K., Farah Hatem Khorsheed, Ali Subhi Alhumaima, Ali J. Ramadhan, Kilan M. Hussien, and Hussein Alkattan. "Intelligent Particle Swarm Optimization Method for Parameter Selecting in Regularization Method for Integral Equation." BIO Web of Conferences 97 (2024): 00039. http://dx.doi.org/10.1051/bioconf/20249700039.

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We use the Tikhonov method as a regularization technique for solving the integral equation of the first kind with noisy and noise-free data. Following that, we go over how to choose the Tikhonov regularization parameter by implementing the Intelligent Piratical Swarm Optimization (IPOS) technique. The effectiveness of combining these two approaches IPOS and Tikhonov is demonstrated to be highly practicable.
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Hämarik, Uno, Reimo Palm, and Toomas Raus. "EXTRAPOLATION OF TIKHONOV REGULARIZATION METHOD." Mathematical Modelling and Analysis 15, no. 1 (2010): 55–68. http://dx.doi.org/10.3846/1392-6292.2010.15.55-68.

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We consider regularization of linear ill‐posed problem Au = f with noisy data fδ, ¦fδ - f¦≤ δ . The approximate solution is computed as the extrapolated Tikhonov approximation, which is a linear combination of n ≥ 2 Tikhonov approximations with different parameters. If the solution u* belongs to R((A*A) n ), then the maximal guaranteed accuracy of Tikhonov approximation is O(δ 2/3) versus accuracy O(δ 2n/(2n+1)) of corresponding extrapolated approximation. We propose several rules for choice of the regularization parameter, some of these are also good in case of moderate over‐ and underestimat
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Yang, Xiao-Juan, and Li Wang. "A modified Tikhonov regularization method." Journal of Computational and Applied Mathematics 288 (November 2015): 180–92. http://dx.doi.org/10.1016/j.cam.2015.04.011.

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Fuhry, Martin, and Lothar Reichel. "A new Tikhonov regularization method." Numerical Algorithms 59, no. 3 (2011): 433–45. http://dx.doi.org/10.1007/s11075-011-9498-x.

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Fang, Sheng, Kui Ying, Jianping Cheng, et al. "Parallel magnetic resonance imaging using wavelet-based multivariate regularization." Journal of X-Ray Science and Technology: Clinical Applications of Diagnosis and Therapeutics 18, no. 2 (2010): 145–55. http://dx.doi.org/10.3233/xst-2010-025000250.

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The parallel imaging technique reduces the scan time at the expense of increased noise, due to its ill-conditioned system matrix. Tikhonov regularization has been proposed for SENSE to reduce the noise. However, Tikhonov regularized images suffer from residual aliasing aritfacts or image blurring when a low resolution prior image is used. This study used wavelet-based multivariate regularization to overcome this problem, while maintaining the computational efficiency of Tikhonov regularization. In this method, SENSE is formularized as a multilevel-structured problem in the wavelet domain. Regu
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Xue, Xuemin, and Xiangtuan Xiong. "A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation." Mathematics 9, no. 18 (2021): 2255. http://dx.doi.org/10.3390/math9182255.

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In this paper, the numerical analytic continuation problem is addressed and a fractional Tikhonov regularization method is proposed. The fractional Tikhonov regularization not only overcomes the difficulty of analyzing the ill-posedness of the continuation problem but also obtains a more accurate numerical result for the discontinuity of solution. This article mainly discusses the a posteriori parameter selection rules of the fractional Tikhonov regularization method, and an error estimate is given. Furthermore, numerical results show that the proposed method works effectively.
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Yang, Suhua, Xingjun Luo, Chunmei Zeng, Zhihai Xu, and Wenyu Hu. "On the Parameter Choice in the Multilevel Augmentation Method." Computational Methods in Applied Mathematics 20, no. 3 (2020): 555–71. http://dx.doi.org/10.1515/cmam-2018-0189.

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AbstractIn this paper, we apply the multilevel augmentation method for solving ill-posed Fredholm integral equations of the first kind via iterated Tikhonov regularization method. The method leads to fast solutions of the discrete regularization methods for the equations. The convergence rates of iterated Tikhonov regularization are achieved by using a modified parameter choice strategy. Finally, numerical experiments are given to illustrate the efficiency of the method.
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Throne, Robert, and Lorraine Olson. "The Steady Inverse Heat Conduction Problem: A Comparison of Methods With Parameter Selection." Journal of Heat Transfer 123, no. 4 (2001): 633–44. http://dx.doi.org/10.1115/1.1372193.

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In the past we have developed the Generalized Eigensystem GESL techniques for solving inverse boundary value problems in steady heat conduction, and found that these vector expansion methods often give superior results to those obtained with standard Tikhonov regularization methods. However, these earlier comparisons were based on the optimal results for each method, which required that we know the true solution to set the value of the regularization parameter (t) for Tikhonov regularization and the number of mode clusters Nclusters for GESL. In this paper we introduce a sensor sensitivity met
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Dissertations / Theses on the topic "Tikhonov regularization method"

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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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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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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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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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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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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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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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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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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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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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Books on the topic "Tikhonov regularization method"

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Chance, Kelly, and Randall V. Martin. Data Fitting. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199662104.003.0011.

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This chapter explores several of the most common and useful approaches to atmospheric data fitting as well as the process of using air mass factors to produce vertical atmospheric column abundances from line-of-sight slant columns determined by data fitting. An atmospheric spectrum or other type of atmospheric sounding is usually fitted to a parameterized physical model by minimizing a cost function, usually chi-squared. Linear fitting, when the model of the measurements is linear in the model parameters is described, followed by the more common nonlinear fitting case. For nonlinear fitting, t
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Book chapters on the topic "Tikhonov regularization method"

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Peng, Chengbin, William L. Rodi, and M. Nafi Toksöz. "A Tikhonov Regularization Method for Image Reconstruction." In Acoustical Imaging. Springer US, 1993. http://dx.doi.org/10.1007/978-1-4615-2958-3_21.

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Ang, Dang Dinh, Rudolf Gorenflo, Vy Khoi Le, and Dang Duc Trong. "2. Regularization of moment problems by truncated expansion and by the Tikhonov method." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-540-45658-2_3.

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Peng, Yamian, Lichao Feng, Ying Yan, and Huancheng Zhang. "Research of Tikhonov Regularization Method for Solving the First Type Fredholm Integral Equation." In Communications in Computer and Information Science. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16339-5_50.

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Pan, Jianghuai. "Multi-station Passive Pure Direction Finding Cross Localization Method Based on Tikhonov Regularization." In Proceedings of 2022 10th China Conference on Command and Control. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-6052-9_27.

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Retamoso, Mario R., Haroldo F. de Campos Velho, and Marco T. Vilhena. "Estimation of Boundary Conditions from Different Experimental Data Using the LTSN Method and Tikhonov Regularization." In Integral Methods in Science and Engineering. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0111-3_33.

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You, Lei. "The Weighted Generalized Solution Tikhonov Regularization Method for Cauchy Problem for the Modified Helmholtz Equation." In Communications in Computer and Information Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22418-8_48.

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Barkalov, Konstantin, Marina Usova, Leniza Enikeeva, Dmitry Dubovtsev, and Irek Gubaydullin. "Parallel Computing in the Tikhonov Regularization Method for Solving the Inverse Problem of Chemical Kinetics." In Communications in Computer and Information Science. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-38864-4_12.

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Mochurad, Lesia, Khrystyna Shakhovska, and Sergio Montenegro. "Parallel Solving of Fredholm Integral Equations of the First Kind by Tikhonov Regularization Method Using OpenMP Technology." In Advances in Intelligent Systems and Computing IV. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-33695-0_3.

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Chamorro-Servent, Judit, Rémi Dubois, Mark Potse, and Yves Coudière. "Improving the Spatial Solution of Electrocardiographic Imaging: A New Regularization Parameter Choice Technique for the Tikhonov Method." In Functional Imaging and Modelling of the Heart. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59448-4_28.

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Jiang, Y., W. Hong, D. Farina, and O. Dössel. "Solving the Inverse Problem of Electrocardiography in a Realistic Environment Using a Spatio-Temporal LSQR-Tikhonov Hybrid Regularization Method." In IFMBE Proceedings. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03879-2_228.

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Conference papers on the topic "Tikhonov regularization method"

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Jeyamohan, Kunaratnam, Tommy H. T. Chan, Khac-Duy Nguyen, and David P. Thambiratnam. "Computation-Effective Method for Prestress Force and Moving Force Identification." In IABSE Symposium, Tokyo 2025: Environmentally Friendly Technologies and Structures: Focusing on Sustainable Approaches. International Association for Bridge and Structural Engineering (IABSE), 2025. https://doi.org/10.2749/tokyo.2025.2336.

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&lt;p&gt;Structural health monitoring (SHM) of existing prestressed concrete bridges (PCBs) is of paramount importance due to the direct impact of failures on the safety of the bridge users. Numerous studies have been conducted to identify the existing prestress force and moving force, however, most of the methods face practical challenges and suffer from inherent ill‐conditioning. Considering these issues, this study proposes a load shape function (LSF)‐based approach for the synergic identification of prestress force and moving force in continuously supported PCBs. Through numerical studies,
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Haeusele, Jakob, Clemens Schmid, Josepha Hilmer, et al. "A novel phase retrieval method for continuously acquired grating-based dark-field computed tomography using Tikhonov regularization." In Quantitative Phase Imaging XI, edited by YongKeun Park and Yang Liu. SPIE, 2025. https://doi.org/10.1117/12.3040198.

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Cai, Pengfei, Pan Zhou, Tuo Shi, and Jianglin Shao. "Tikhonov regularization method for dynamic load identification." In Fourth International Conference on Artificial Intelligence and Electromechanical Automation (AIEA 2023), edited by Fushuan Wen, chuanjun Zhao, and Yanjiao Chen. SPIE, 2023. http://dx.doi.org/10.1117/12.2684938.

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Lamm, Patricia K. "On the Local Regularization of Inverse Problems of Volterra Type." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0664.

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Abstract We consider a local regularization method for the solution of first-kind Volterra integral equations with convolution kernel. The local regularization is based on a splitting of the original Volterra operator into “local” and “global” parts, and a use of Tikhonov regularization to stabilize the inversion of the local operator only. The regularization parameters for the local procedure include the standard Tikhonov parameter, as well as a parameter that represents the length of the local regularization interval. We present a convergence theory for the infinite-dimensional regularizatio
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Daun, K. J., K. A. Thomson, F. Liu, and G. J. Smallwood. "Solution of Abel’s Integral Equation Using Tikhonov Regularization." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81430.

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This paper presents a method based on Tikhonov regularization for solving one-dimensional inverse tomography problems that arise in combustion applications. In this technique, Tikhonov regularization transforms the ill-conditioned set of equations generated by onion-peeling deconvolution into a well-conditioned set that is more stable to measurement errors that arise in experimental settings. The performance of this method is compared to that of onion-peeling and Abel three-point deconvolution by solving for a known field variable distribution from projected data contaminated with artificially
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Wu, Menglu, and Xiaolin Chen. "Tikhonov Regularization Methods for the Inverse Scalp Electroencephalography." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10538.

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Electroencephalography (EEG) source localization of brain activity is of high diagnostic value. Noninvasive numerical procedures can be developed to help reconstruct the cortical brain activities from the low-spatial-resolution scalp EEG measurement. In this paper, Tikhonov regularization methods are employed to tackle the solution difficulty associated with the ill-posed reconstruction problem. Three different techniques, namely the L-curve method, the generalized cross validation (GCV) and the discrepancy principle (DP), are implemented to help identify an optimum parameter for the numerical
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Feng, Baobin, Wenjuan Wang, and Junxing Cao. "An Improved Tikhonov Regularization Method for Conductivity Tomography Imaging." In 2008 International Symposium on Computer Science and Computational Technology. IEEE, 2008. http://dx.doi.org/10.1109/iscsct.2008.330.

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Wang, Lei, Hong-ming Li, and Xiao-tong Du. "WSN multilateral localization algorithm based on Tikhonov regularization method." In International Symposium on Instrumentation Science and Technology, edited by Jiubin Tan and Xianfang Wen. SPIE, 2008. http://dx.doi.org/10.1117/12.810238.

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Fang, Jingying, Feihu Zheng, Shijie Chen, and Yewen Zhang. "Tikhonov Regularization Algorithm for Thermal Pulse Method Data Analysis." In 2023 IEEE 4th International Conference on Electrical Materials and Power Equipment (ICEMPE). IEEE, 2023. http://dx.doi.org/10.1109/icempe57831.2023.10139634.

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Zhang, Q., P. An, Z. Y. Zhang, and Qiuwen Zhang. "New intermediate view synthesis method based on Tikhonov regularization." In 2010 10th International Conference on Signal Processing (ICSP 2010). IEEE, 2010. http://dx.doi.org/10.1109/icosp.2010.5655504.

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