• 한국방사선학회논문지
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• 제11권7호
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• pp.679-685
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• 2017

환자의 병변 진단에 효과적인 CT 검사가 광범위하게 실시되고 있어, 방사선 피폭이 매우 크게 증가하였다. 환자의 피폭 선량을 줄이기 위해 다양한 방법이 강구되고 있고, 영상재구성 측면에서 반복 재구성 기법이 적용되고 있다. 반복 재구성 기법 중 대수적 재구성 기법의 정규화 인자에 대한 재구성된 단면 영상의 품질을 정규화 제곱평균제곱근 오차를 이용하여 조사하였다. 프로그램은 Visual C++로 작성하였으며 평행빔하에서 $512{\times}512$ 크기의 Shepp-Logan 두부 팬텀, 360장의 투영 영상, 1024개의 검출기 픽셀을 적용하였고, 전방투영과 역투영에 Joseph 방법을 사용하였다. 0.09-0.12의 정규화 인자에서 10회 반복으로 최소의 NRMS값 0.108을 얻었고 0.1% 및 0.2%의 잡음에 대해 8회 및 6회에서 최적의 영상을 보였다. 사용하는 팬텀에 따라 최적화된 값의 변동이 관찰되어 ART를 사용할 경우 정규화 인자에 대해서는 case-by-case로 최적의 값을 찾아야 한다는 것을 알 수 있다. 대수적 재구성 기법에서 최적의 정규화 인자를 발견함으로써 단면 영상을 획득하는데 걸리는 시간을 단축할 수 있을 것이다.

• 충청수학회지
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• 제32권1호
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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.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 신호처리소사이어티 추계학술대회 논문집
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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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• 제6권2호
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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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• 제44권5호
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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.

• 대한수학회지
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• 제55권4호
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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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• 제32권1호
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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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• 제27권5호
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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.

• 정보처리학회논문지B
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• 제14B권4호
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• pp.241-248
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• 2007

본 논문은 광학 흐름을 추정하는데 있어서 최적 정규화 매개변수를 결정하기 위한 L-curve 모서리 검출 방법을 제안한다. 기존의 곡률법은 L-curve의 곡률 그래프에서 최대 위치를 찾는 반면, 제안한 방법은 바로 우측 음의 계곡과의 곡률 차가 최대가 되는 양의 봉우리의 위치를 찾아서 매개변수 값을 결정한다. 이 방법으로 선정한 매개변수로 광학 흐름을 추정하면, 평균적으로 최소 오차로부터 단지 0.02 pixel/frame 차이가 나는 것이 실험을 통하여 보여진다. 또한 제안한 방법으로 기존의 모서리 검출법인 곡률법이나 적응 제거법에 비해 최소 오차에 가장 가까운 광학 흐름을 구할 수 있었다.

• 한국해양공학회지
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• 제22권4호
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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.