• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.505-516
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• 2020

This study shows that image deblurring problems can be transformed into the multi-parameter Tikhonov type with multiple right hand sides. Also, this paper proposes the extension of the global generalized cross validation to obtain an appropriate choice of the regularization parameters for this problem. The experimental results of using the preconditioned Gl-CGLS algorithm were analyzed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.9-24
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• 2002

Total Variation(TV) regularization method is effective for reconstructing "blocky", discontinuous images from contaminated image with noise. But TV is represented by highly nonlinear integro-differential equation that is hard to solve. There have been much effort to obtain stable and fast methods. C. Vogel introduced "the Fixed Point Lagged Diffusivity Iteration", which solves the nonlinear equation by linearizing. In this paper, we apply multigrid(MG) method for cell centered finite difference (CCFD) to solve system arise at each step of this fixed point iteration. In numerical simulation, we test various images varying noises and regularization parameter $\alpha$ and smoothness $\beta$ which appear in TV method. Numerical tests show that the parameter ${\beta}$ does not affect the solution if it is sufficiently small. We compute optimal $\alpha$ that minimizes the error with respect to $L^2$ norm and $H^1$ norm and compare reconstructed images.

• Journal of Biomedical Engineering Research
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• v.18 no.3
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• pp.211-216
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• 1997

An inverse method with regularization has been developed to determine the viscoelastic properties of trabecular bone. A series of stress relaxation experiments were performed under the condition of uniaxial compression stress state. Optimization has been formulated within the framework of nonlinear least-squares and a modified Gauss-Newton method with a zeroth-order regularization technique. The stress relaxation behavior of trabecular bone was analyzed using a standard viscoelastic model. The present study clearly shows that trabecular bone exhibits typical viscoelastic stress relaxation behavior, and the obtained material parameters well represent the viscoelastic behavior of trabecular bone.

• Proceedings of the Korean Vacuum Society Conference
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• 2010.02a
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• pp.472-472
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• 2010

The tomography has played a key role in tokamak plasma diagnostics for image reconstruction. The Phillips-Tikhonov (P-T) regularization method was attempted in this work to reconstruct cross-sectional phantom images of the plasma by minimizing the gradient between adjacent pixel data. Recent studies about the comparison of the several tomographic reconstruction methods showed that the P-T method produced more accurate results. We have studied existing Laplacian matrix used in Phillips-Tikhonov regularization method and developed modified Laplacian matrix (Modified L). The comparison of the reconstruction result by the modified L and existing L showed that modified L produced more accurate result. The difference was significantly pronounced when a portion of plasma was reconstructed. These results can be utilized in the Edge Plasma diagnostics; especially in divertor diagnostics on tokamak a large impact is expected. In addition, accurate reconstruction results from received data in only one direction were confirmed through phantom test by using P-T method with modified L. These results can be applied to the tangentially viewing pin-hole camera diagnostics on tokamak.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.1
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• pp.161-166
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• 2020

This paper suggests an extension of the unified Bayesian Tikhonov regularization method. The unified method establishes the relationship between Tikhonov regularization parameter and Bayesian hyper-parameters, and presents a formula for obtaining the regularization parameter using the maximum posterior probability and the evidence framework. When the dimension of the data matrix is m by n (m >= n), we derive that the total misfit has the range of m ± n instead of m. Thus the search range is extended from one to 2n + 1 integer points. Golden section search rather than linear one is applied to reduce the time. A new benchmark for optimizing relative error and new model selection criteria to target it are suggested. The experimental results show the effectiveness of the proposed method in the image restoration problem.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.18 no.10
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• pp.75-80
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• 2017

In this paper, we describe the effect of the regularization method and the network with identity mapping on the performance of the activation functions in deep convolutional neural networks. The activation functions act as nonlinear transformation. In early convolutional neural networks, a sigmoid function was used. To overcome the problem of the existing activation functions such as gradient vanishing, various activation functions were developed such as ReLU, Leaky ReLU, parametric ReLU, and ELU. To solve the overfitting problem, regularization methods such as dropout and batch normalization were developed on the sidelines of the activation functions. Additionally, data augmentation is usually applied to deep learning to avoid overfitting. The activation functions mentioned above have different characteristics, but the new regularization method and the network with identity mapping were validated only using ReLU. Therefore, we have experimentally shown the effect of the regularization method and the network with identity mapping on the performance of the activation functions. Through this analysis, we have presented the tendency of the performance of activation functions according to regularization and identity mapping. These results will reduce the number of training trials to find the best activation function.

• Structural Engineering and Mechanics
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• v.55 no.6
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• pp.1157-1176
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• 2015

This study presents optimizing structural topology patterns using regularization of Heaviside function. The present method needs not filtering process to typical SIMP method. Using the penalty formulation of the SIMP approach, a topology optimization problem is formulated in co-operation, i.e., couple-signals, with design variable values of discrete elements and a regularized Heaviside step function. The regularization of discontinuous material distributions is a key scheme in order to improve the numerical problems of material topology optimization with 0 (void)-1 (solid) solutions. The weak forms of an equilibrium equation are expressed using a coupled regularized Heaviside function to evaluate sensitivity analysis. Numerical results show that the incorporation of the regularized Heaviside function and the SIMP leads to convergent solutions. This method is tested using several examples of a linear elastostatic structure. It demonstrates that improved optimal solutions can be obtained without the additional use of sensitivity filtering to improve the discontinuous 0-1 solutions, which have generally been used in material topology optimization problems.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.353-369
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• 2024

In this study, we investigate the unknown time-dependent heat source function in inverse problems. We consider three general nonlocal conditions; two classical boundary conditions and one nonlocal over-determination, condition, these genereate six different cases. The finite integration method (FIM), based on numerical integration, has been adapted to solve PDEs, and we use it to discretize the spatial domain; we use backward differences for the time variable. Since the inverse problem is ill-posed with instability, we apply regularization to reduce the instability. We use the first-order Tikhonov's regularization together with the minimization process to solve the inverse source problem. Test examples in all six cases are presented in order to illustrate the accuracy and stability of the numerical solutions.

• Journal of Ocean Engineering and Technology
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• v.22 no.4
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• pp.1-7
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• 2008

The primary aim of the paper is to solve an unstable axisymmetric initial value problem of wave propagation when given initial data that is deteriorated by noise such as measurement error. To overcome the instability of the problem, Tikhonov's regularization, known as a non-iterative numerical regularization method, is introduced to solve the problem. The L-curvecriterion is introduced to find the optimal regularization parameter for the solution. It is confirmed that fairly stable solutions are realized and that they are accurate when compared to the exact solution.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.340-347
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• 2003

The aim of regularization of a structural configuration is to obtain a structure that consists of elements with identical or nearly identical length. And it is also possible to modify the configuration in a manner that the size of the elements vary in accordance with a specified pattern. For practical purpose, geodesic dome is cut off at a suitable place in order to make it fit on horizontal. Inevitably this pattern effects a change of element lengths. The purpose of this study is to verify a method for regularization of structural configuration by genetic algorithms and modify the element lengths of the dome. As a result of regularization of domes with various rise-span ratio, modified configurations have more regular element lengths and are more economical than initial configurations.