• Journal of the Korean Society of Radiology
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• v.11 no.7
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• pp.679-685
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• 2017

Computed tomography has widely been used to diagnose patient disease, and patient dose also increase rapidly. To reduce the patient dose by CT, various techniques have been applied. The iterative reconstruction is used in view of image reconstruction. Image quality of the reconstructed section image through algebraic reconstruction technique, one of iterative reconstruction methods, was examined by the normalized root mean square error. The computer program was written with the Visual C++ under the parallel beam geometry, Shepp-Logan head phantom of $512{\times}512$ size, projections of 360, and detector-pixels of 1,024. The forward and backward projection was realized by Joseph method. The minimum NRMS of 0.108 was obtained after 10 iterations in the regularization parameter of 0.09-0.12, and the optimum image was obtained after 8 and 6 iterations for 0.1% and 0.2% noise. Variation of optimum value of the regularization parameter was observed according to the phantom used. If the ART was used in the reconstruction, the optimal value of the regularization parameter should be found in the case-by-case. By finding the optimal regularization parameter in the algebraic reconstruction technique, the reconstruction time can be reduced.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.149-156
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• 2019

This paper present the global generalized cross validation as the appropriate choice of the regularization parameter in the preconditioned Gl-LSQR method in solving image deblurring problems. The regularization parameter, chosen from the global generalized cross validation, with preconditioned Gl-LSQR method can give better reconstructions of the true image than other parameters considered in this study.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.489-492
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• 2003

In this paper, we propose an iterative mixed norm image restoration algorithm using multi regularization parameters. A functional which combines the regularized l$_2$ norm functional and the regularized l$_4$ functional is proposed. The smoothness of each functional is determined by the regularization parameters. Also, a regularization parameter is used to determine the relative importance between the regularized l$_2$ functional and the regularized l$_4$ functional. An iterative algorithm is utilized for obtaining a solution and its convergence is 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.

• Structural Engineering and Mechanics
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• v.44 no.5
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• pp.585-600
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• 2012

This paper presents a Modified Tikhonov Regularization (MTR) method in model updating for damage identification with model errors and measurement noise influences consideration. The identification equation based on sensitivity approach from the dynamic responses is ill-conditioned and is usually solved with regularization method. When the structural system contains model errors and measurement noise, the identified results from Tikhonov Regularization (TR) method often diverge after several iterations. In the MTR method, new side conditions with limits on the identification of physical parameters allow for the presence of model errors and ensure the physical meanings of the identified parameters. Chebyshev polynomial is applied to approximate the acceleration response for moderation of measurement noise. The identified physical parameter can converge to a relative correct direction. A three-dimensional unsymmetrical frame structure with different scenarios is studied to illustrate the proposed method. Results revealed show that the proposed method has superior performance than TR Method when there are both model errors and measurement noise in the structure system.

• 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.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.535-546
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• 2020

In genetic association studies, pleiotropy is a phenomenon where a variant or a genetic region affects multiple traits or diseases. There have been many studies identifying cross-phenotype genetic associations. But, most of statistical approaches for detection of pleiotropy are based on individual tests where a single variant association with multiple traits is tested one at a time. These approaches fail to account for relations among correlated variants. Recently, multivariate regularization methods have been proposed to detect pleiotropy in analysis of high-dimensional genomic data. However, they suffer a problem of tuning parameter selection, which often results in either too many false positives or too small true positives. In this article, we applied selection probability to multivariate regularization methods in order to identify pleiotropic variants associated with multiple phenotypes. Selection probability was applied to individual elastic-net, unified elastic-net and multi-response elastic-net regularization methods. In simulation studies, selection performance of three multivariate regularization methods was evaluated when the total number of phenotypes, the number of phenotypes associated with a variant, and correlations among phenotypes are different. We also applied the regularization methods to a wild bean dataset consisting of 169,028 variants and 17 phenotypes.

• The KIPS Transactions:PartB
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• v.14B no.4
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• pp.241-248
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• 2007

An L-curve corner detection method is proposed for the determination of the regularization parameter in optical flow estimation. The method locates the positive peak whose curvature difference from the just right-hand negative valley is the maximum in the curvature plot of the L-curve. while the existing curvature-method simply finds the maximum in the plot. Experimental results show that RMSE of the estimated optical flow is greater only by 0.02 pixels-per-frame than the least in the average sense. The proposed method is also compared with an existing curvature-method and the adaptive pruning method, resulting in the optical flow estimation closest to the least RMSE.

• 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.