• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.117-128
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• 2017

As an efficient way to determine the regularization parameter in the discrete ill-posed problems with multiple right-hand sides, we suggest global L-curve criterion as an extension of L-curve technique for image restoration problems with single right-hand side.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.23-37
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• 2011

In this paper, we use a modified Tikhonov regularization method to solve the Fredholm integral equation of the first kind. Under the assumption that measured data are contaminated with deterministic errors, we give two error estimates. The convergence rates can be obtained under the suitable choices of regularization parameters and the number of measured points. Some numerical experiments show that the proposed method is effective and stable.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.3027-3032
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• 2007

To understand the complex phenomena performed in steam explosion, the fast and global measurement of the steam distribution is imperative for this extremely rapid transient stimulation of the bubble breakup and coalescence due to turbulent eddies and shock waves. TROI, the experimental facility requests more robust sensor system to meet this requirement. In Europe, researchers are prefer a X-ray method but this method is very expensive and has limited measurement range. There is an alternative technology such as ECT. Because of TROI's geometry, however, we need axial tomography method. This paper reviews image reconstruction algorethms for axial tomography, including Tikhonov regularization and iterative Tikhonov regularization. Axial tomography method is examined by simulation and experiment for typical permittivity distributions. Future works in axial tomography technology is discussed.

• Smart Structures and Systems
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• v.18 no.5
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• pp.839-864
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• 2016

This paper presents an efficient method for updating the structural finite element model. Model updating is performed through minimizing the difference between the recorded acceleration of a real damaged structure and a hypothetical damaged one. This is performed by updating physical parameters (module of elasticity in this study) in each step using iterative process of modified nonlinear conjugate gradient (M-NCG) and modified Broyden-Fletcher-Goldfarb-Shanno algorithm (M-BFGS) separately. These algorithms are based on sensitivity analysis and provide a solution for nonlinear damage detection problem. Three illustrative test examples are considered to assess the performance of the proposed method. Finally, it is demonstrated that the proposed method is satisfactory for detecting the location and ratio of structural damage in presence of noise.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1905-1926
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• 2017

In this paper we introduce a new iterative method by the combination of the prox-Tikhonov regularization and the alternating resolvents for finding a common zero of two accretive operators in Banach spaces. And we will give some applications and numerical examples. The results of this paper improve and extend the corresponding results announced by many others.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.849-875
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• 2018

The purpose of this paper is to present an operator method of regularization for the problem of finding a solution of a system of nonlinear ill-posed equations with a monotone hemicontinuous mapping and N inverse-strongly monotone mappings in Banach spaces. A regularization parameter choice is given and convergence rate of the regularized solutions is estimated. We also give the convergence and convergence rate for regularized solutions in connection with the finite-dimensional approximation. An iterative regularization method of zero order in a real Hilbert space and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.

• East Asian mathematical journal
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• v.32 no.1
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• pp.129-138
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• 2016

In this paper, we propose an efficient regularization technique (The Method of Regularized Ratios) for the reconstruction of the shape of a rigid elastic scatterer from far field measurements. The approach used is based on the factorization method and creates via Picard's condition ratios, baptized Regularized Ratios, that serve to effectively remove unwanted singular values that may lead to poor reconstructions. This is achieved through the use of a sophisticated algorithm that progressively adjusts an initially set moderate tolerance. In comparison with the well established Tikhonov-Morozov regularization techniques our new algorithm appears to be more computationally efficient as it doesn't require computation of the regularization parameter for each point in the grid.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.675-688
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• 2014

In this paper, we present an efficient way to determine a suitable value of the regularization parameter using the global generalized cross validation and analyze the experimental results from preconditioned global conjugate gradient linear least squares(Gl-CGLS) method in solving image deblurring problems. Preconditioned Gl-CGLS solves general linear systems with multiple right-hand sides. It has been shown in [10] that this method can be effectively applied to image deblurring problems. The regularization parameter, chosen from the global generalized cross validation, with preconditioned Gl-CGLS method can give better reconstructions of the true image than other parameters considered in this study.

• Journal of IKEEE
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• v.5 no.2 s.9
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• pp.153-163
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• 2001

Electrical impedance tomography(EIT) is a relatively new imaging modality in which the internal impedivity distribution is reconstructed based on the known sets of injected currents and measured voltages on the surface of the object. We describe a dynamic EIT imaging technique for the case where the resistivity distribution inside the object changes rapidly within the time taken to acquire a full set of independent measurement data. In doing so, the inverse problem is treated as the state estimation problem and the unknown state (resistivity) is estimated with the aid of extended Kalman filter in a minimum mean square error sense. In particular, additional electrodes are attached to the known internal structure of the object to enhance the reconstruction performance and modified Tikhonov regularization technique is employed to mitigate the ill-posedness of the inverse problem. Computer simulations are provided to illustrate the reconstruction performance of the proposed algorithm.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.59-71
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• 2016

To obtain more accurate approximation of the true images in the deblurring problems, the weighted global generalized cross validation(GCV) function to the inverse problem with multiple right-hand sides is suggested as an efficient way to determine the regularization parameter. We analyze the experimental results for many test problems and was able to obtain the globally useful range of the weight when the preconditioned global conjugate gradient linear least squares(Gl-CGLS) method with the weighted global GCV function is applied.