• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.353-363
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• 2013

A variant of the global conjugate gradient method for solving general linear systems with multiple right-hand sides is proposed. This method is called as the global conjugate gradient linear least squares (Gl-CGLS) method since it is based on the conjugate gradient least squares method(CGLS). We present how this method can be implemented for the image deblurring problems with Neumann boundary conditions. Numerical experiments are tested on some blurred images for the purpose of comparing the computational efficiencies of Gl-CGLS with CGLS and Gl-LSQR. The results show that Gl-CGLS method is numerically more efficient than others for the ill-posed problems.

• 충청수학회지
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• 제27권4호
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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.

• 충청수학회지
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• 제29권1호
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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.

• 한국통신학회논문지
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• 제41권1호
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• pp.83-85
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• 2016

LS 신호검출 OFDM은 채널 행렬이 불량 조건이 될 확률이 증가하여 고속 시변 채널에서 성능이 저하된다. LS 신호검출의 성능저하를 방지하기 위하여 다양한 안정화 방식이 적용되고 있다. 본 논문에서는 변조방식의 특성이 반영된 실행중지 기준을 적용한 CGLS 방식을 제안하였으며 최적의 LMMSE에 근접한 성능을 얻을 수 있었다.

• 충청수학회지
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• 제33권4호
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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 applied mathematics & informatics
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• 제36권3_4호
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• pp.317-330
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• 2018

We first provide how to apply the global preconditioned conjugate gradient ($G{\ell}-PCG$) method with Kronecker product preconditioners to image deblurring problems with nearly separable point spread functions. We next provide a coarse-grained parallel image deblurring algorithm using the $G{\ell}-PCG$. Lastly, we provide numerical experiments for image deblurring problems to evaluate the effectiveness of the $G{\ell}-PCG$ with Kronecker product preconditioner by comparing its performance with those of the $G{\ell}-CG$, CGLS and preconditioned CGLS (PCGLS) methods.

• 충청수학회지
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• 제30권1호
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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.

• 충청수학회지
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• 제24권4호
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• pp.895-903
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• 2011

A two dimensional version of LSQR iterative algorithm which takes advantages of working solely with the 2-dimensional arrays is developed and applied to the image deblurring problem. The efficiency of the method comparing to the Fourier-based LSQR method and the 2-D version CGLS algorithm methods proposed by Hanson ([4]) is analyzed.

• 대한수학회지
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• 제52권2호
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• pp.349-372
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• 2015

This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.

• Corrosion Science and Technology
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• 제7권1호
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• pp.1-5
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• 2008

The gas atmosphere in continuous annealing and galvanizing lines alters both composition and microstructure of the surface and sub-surface of sheet steel. The formation and morphology of the oxides of alloying elements in High Strength Interstitial Free (HS-IF), Dual Phase (DP) and Transformation-Induced Plasticity (TRIP) steels are strongly influenced by the furnace dew point, and the presence of specific oxide may result in surface defects and bare areas on galvanized sheet products. The present contribution reviews the progress made recently in understanding the selective formation of surface and subsurface oxides during annealing in hot dip galvanizing and conventional continuous annealing lines. It is believed that the surface and sub-surface composition and microstructure have a pronounced influence on galvanized sheet product surface quality. In the present study, it is shown that the understanding of the relevant phenomena requires a combination of precise laboratory-scale simulations of the relevant technological processes and the use of advanced surface analytical tools.