• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.177-186
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• 2009

The global least squares method (Gl-LSQR) is a generalization of LSQR method for solving linear system with multiple right hand sides. In this paper, we present how to apply this algorithm for solving the image restoration problem and illustrate the usefulness and effectiveness of this method from numerical experiments.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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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.

• The Magazine of the IEIE
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• v.38 no.1
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• pp.31-43
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• 2011

The mathematical foundations of the compressive sensing which goes against the common wisdom of data acquisition (the Nyquist-Shannon theorem) is reviewed. The compressive sensing asserts that one can reconstruct images or signals of interest accurately from a number of samples far smaller than the desired resolution of the image (e.g., the number of pixels in the image). The compressive sensing has far reaching implications. It suggests the new data acquisition protocols that translates analog information to digital form with fewer sensors considered necessary.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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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.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.535-559
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• 2022

The notions of cubic intuitionistic fuzzy set to filters and implicative filters of BE-algebras are introduced. Relations between cubic intuitionistic fuzzy filters with cubic intuitionistic fuzzy implicative filters of BE-algebras are investigated. The homomorphic image and inverse image of cubic intuitionistic fuzzy filters are studied and some related properties are investigated. Also, the product of cubic intuitionistic fuzzy subalgebras (implicative filters) of BE-algebras are investigated.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.175-182
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• 2009

Microscopic imaging system often requires the algorithm to adjust location of camera lenses automatically in machine level. An effort to detect the best focal point is naturally interpreted as a mathematical inverse problem [1]. Following Wiener's point of view [2], we interpret the focus level of images as the quantified factor appeared in image degradation model: g = $f{\ast}H+{\eta}$, a standard mathematical model for understanding signal or image degradation process [3]. In this paper we propose a simple, very fast and robust method to compare the degradation parameters among the multiple images given by introducing outlier analysis of histogram.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.719-734
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• 2018

An image restoration problem with Poisson noise arises in many applications of medical imaging, astronomy, and microscopy. To overcome ill-posedness, Total Variation (TV) model is commonly used owing to edge preserving property. Since staircase artifacts are observed in restored smooth regions, higher-order TV regularization is introduced. However, sharpness of edges in the image is also attenuated. To compromise benefits of TV and higher-order TV, the weighted sum of the non-convex TV and non-convex higher order TV is used as a regularizer in the proposed variational model. The proposed model is non-convex and non-smooth, and so it is very challenging to solve the model. We propose an iterative reweighted algorithm with the proximal linearized alternating direction method of multipliers to solve the proposed model and study convergence properties of the algorithm.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.2
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• pp.129-142
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• 2014

We propose a variational segmentation model based on statistical information of intensities in an image. The model consists of both a local region-based energy and a global region-based energy in order to handle misclassification which happens in a typical statistical variational model with an assumption that an image is a mixture of two Gaussian distributions. We find local ambiguous regions where misclassification might happen due to a small difference between two Gaussian distributions. Based on statistical information restricted to the local ambiguous regions, we design a local region-based energy in order to reduce the misclassification. We suggest an algorithm to avoid the difficulty of the Euler-Lagrange equations of the proposed variational model.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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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.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.10
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• pp.38-49
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• 1996

In this paper, we propose a fast hierarchical image segmentation using mathematical morphology. The proposed segmentation method is composed of five basic steps; multi-thresholding, open-close by reconstructing, mode operation, marker extraction, and region decision. In the multi-thresholding, an input image is simplified by Lloyd clustering algorithm. The multi-thresholded image then is more simplified by open-close by reconstruction and mode operating. In the region decision, to which region each uncertainty pixel belongs finally is decided by a watershed algorithm. Experimental results show that the quality of the segmentation results by the proposed method is not inferior to that by the conventional method and the average times elapsed by the proposed method can be reduced by one tghird of those elapsed by the conventional method.