• Title/Summary/Keyword: regularization

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An Unified Bayesian Total Variation Regularization Method and Application to Image Restoration (통합 베이즈 총변이 정규화 방법과 영상복원에 대한 응용)

  • Yoo, Jae-Hung
    • The Journal of the Korea institute of electronic communication sciences
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    • v.17 no.1
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    • pp.41-48
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    • 2022
  • This paper presents the unified Bayesian Tikhonov regularization method as a solution to total variation regularization. The integrated method presents a formula for obtaining the regularization parameter by transforming the total variation term into a weighted Tikhonov regularization term. It repeats until the reconstructed image converges to obtain a regularization parameter and a new weighting factor based on it. The experimental results show the effectiveness of the proposed method for the image restoration problem.

Resistivity Image Reconstruction Using Interacting Dual-Mode Regularization (상호작용 이중-모드 조정방법을 이용한 저항률 영상 복원)

  • Kang, Suk-In;Kim, Kyung-Youn
    • Journal of IKEEE
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    • v.20 no.2
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    • pp.152-162
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    • 2016
  • Electrical resistivity tomography (ERT) is a technique to reconstruct the internal resistivity distribution using the measured voltages on the surface electrodes. ERT inverse problem suffers from ill-posedness nature, so regularization methods are used to mitigate ill-posedness. The reconstruction performance varies depending on the type of regularization method. In this paper, an interacting dual-mode regularization method is proposed with two different regularization methods, L1-norm regularization and total variation (TV) regularization, to achieve robust reconstruction performance. The interacting dual-mode regularization method selects the suitable regularization method and combines the regularization methods based on computed mode probabilities depending on the actual conditions. The proposed method is tested with numerical simulations and the results demonstrate an improved reconstruction performance.

ON THREE SPECTRAL REGULARIZATION METHODS FOR A BACKWARD HEAT CONDUCTION PROBLEM

  • Xiong, Xiang-Tuan;Fu, Chu-Li;Qian, Zhi
    • Journal of the Korean Mathematical Society
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    • v.44 no.6
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    • pp.1281-1290
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    • 2007
  • We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective.

Application of Regularization Method to Angle-resolved XPS Data (각분해X-선광전자분광법 데이터 분석을 위한 regularization 방법의 응용)

  • 노철언
    • Journal of the Korean Vacuum Society
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    • v.5 no.2
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    • pp.99-106
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    • 1996
  • Two types of regularization method (singular system and HMP approaches) for generating depth-concentration profiles from angle-resolved XPS data were evaluated. Both approaches showed qualitatively similar results although they employed different numerical algorithms. The application of the regularization method to simulated data demonhstrates its excellent utility for the complex depth profile system . It includes the stable restoration of depth-concentration profiles from the data with considerable random error and the self choice of smoothing parameter that is imperative for the successful application of the regularization method. The self choice of smoothing parameter is based on generalized cross-validation method which lets the data themselves choose the optimal value of the parameter.

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An optimal regularization for structural parameter estimation from modal response

  • Pothisiri, Thanyawat
    • Structural Engineering and Mechanics
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    • v.22 no.4
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    • pp.401-418
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    • 2006
  • Solutions to the problems of structural parameter estimation from modal response using leastsquares minimization of force or displacement residuals are generally sensitive to noise in the response measurements. The sensitivity of the parameter estimates is governed by the physical characteristics of the structure and certain features of the noisy measurements. It has been shown that the regularization method can be used to reduce effects of the measurement noise on the estimation error through adding a regularization function to the parameter estimation objective function. In this paper, we adopt the regularization function as the Euclidean norm of the difference between the values of the currently estimated parameters and the a priori parameter estimates. The effect of the regularization function on the outcome of parameter estimation is determined by a regularization factor. Based on a singular value decomposition of the sensitivity matrix of the structural response, it is shown that the optimal regularization factor is obtained by using the maximum singular value of the sensitivity matrix. This selection exhibits the condition where the effect of the a priori estimates on the solutions to the parameter estimation problem is minimal. The performance of the proposed algorithm is investigated in comparison with certain algorithms selected from the literature by using a numerical example.

An Extension of Possibilistic Fuzzy C-means using Regularization (Regularization을 이용한 Possibilistic Fuzzy C-means의 확장)

  • Heo, Gyeong-Yong;NamKoong, Young-Hwan;Kim, Seong-Hoon
    • Journal of the Korea Society of Computer and Information
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    • v.15 no.1
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    • pp.43-50
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    • 2010
  • Fuzzy c-means (FCM) and possibilistic c-means (PCM) are the two most well-known clustering algorithms in fuzzy clustering area, and have been applied in many applications in their original or modified forms. However, FCM's noise sensitivity problem and PCM's overlapping cluster problem are also well known. Recently there have been several attempts to combine both of them to mitigate the problems and possibilistic fuzzy c-means (PFCM) showed promising results. In this paper, we proposed a modified PFCM using regularization to reduce noise sensitivity in PFCM further. Regularization is a well-known technique to make a solution space smooth and an algorithm noise insensitive. The proposed algorithm, PFCM with regularization (PFCM-R), can take advantage of regularization and further reduce the effect of noise. Experimental results are given and show that the proposed method is better than the existing methods in noisy conditions.

STABILITY ANALYSIS OF REGULARIZED VISCOUS VORTEX SHEETS

  • Sohn, Sung-Ik
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.3
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    • pp.843-852
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    • 2016
  • A vortex sheet is susceptible to the Kelvin-Helmhotz instability, which leads to a singularity at finite time. The vortex blob model provided a regularization for the motion of vortex sheets in an inviscid fluid. In this paper, we consider the blob model for viscous vortex sheets and present a linear stability analysis for regularized sheets. We show that the diffusing viscous vortex sheet is unstable to small perturbations, regardless of the regularization, but the viscous sheet in the sharp limit becomes stable, when the regularization is applied. Both the regularization parameter and viscosity damp the growth rate of the sharp viscous vortex sheet for large wavenumbers, but the regularization parameter gives more significant effects than viscosity.

Performance Comparison of Regularization Methods in Electrical Resistance Tomography (전기 저항 단층촬영법에서의 조정기법 성능비교)

  • Kang, Suk-In;Kim, Kyung-Youn
    • Journal of IKEEE
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    • v.20 no.3
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    • pp.226-234
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    • 2016
  • Electrical resistance tomography (ERT) is an imaging technique where the internal resistivity distribution inside an object is reconstructed. The ERT image reconstruction is a highly nonlinear ill-posed problem, so regularization methods are used to achieve desired image. The reconstruction outcome is dependent on the type of regularization method employed such as l2-norm, l1-norm, and total variation regularization method. That is, use of an appropriate regularization method considering the flow characteristics is necessary to attain good reconstruction performance. Therefore, in this paper, regularization methods are tested through numerical simulations with different flow conditions and the performance is compared.

A Unified Bayesian Tikhonov Regularization Method for Image Restoration (영상 복원을 위한 통합 베이즈 티코노프 정규화 방법)

  • Yoo, Jae-Hung
    • The Journal of the Korea institute of electronic communication sciences
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    • v.11 no.11
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    • pp.1129-1134
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    • 2016
  • This paper suggests a new method of finding regularization parameter for image restoration problems. If the prior information is not available, separate optimization functions for Tikhonov regularization parameter are suggested in the literature such as generalized cross validation and L-curve criterion. In this paper, unified Bayesian interpretation of Tikhonov regularization is introduced and applied to the image restoration problems. The relationship between Tikhonov regularization parameter and Bayesian hyper-parameters is established. Update formular for the regularization parameter using both maximum a posteriori(: MAP) and evidence frameworks is suggested. Experimental results show the effectiveness of the proposed method.

Selection probability of multivariate regularization to identify pleiotropic variants in genetic association studies

  • Kim, Kipoong;Sun, Hokeun
    • 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.