• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.161-197
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• 2020

Total variation minimization is standard in mathematical imaging and there have been numerous researches over the last decades. In order to process large-scale images in real-time, it is essential to design parallel algorithms that utilize distributed memory computers efficiently. The aim of this paper is to illustrate recent advances of domain decomposition methods for total variation minimization as parallel algorithms. Domain decomposition methods are suitable for parallel computation since they solve a large-scale problem by dividing it into smaller problems and treating them in parallel, and they already have been widely used in structural mechanics. Differently from problems arising in structural mechanics, energy functionals of total variation minimization problems are in general nonlinear, nonsmooth, and nonseparable. Hence, designing efficient domain decomposition methods for total variation minimization is a quite challenging issue. We describe various existing approaches on domain decomposition methods for total variation minimization in a unified view. We address how the direction of research on the subject has changed over the past few years, and suggest several interesting topics for further research.

• Health Policy and Management
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• v.3 no.1
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• pp.25-52
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• 1993

Variation in the utilization of medical services is a very important issue in cost containment and quality assurance of health care. Practice variation directly affects health care expenditure especially in fee-for-service system, which is the payment system of health insurance in Korea. In addition to cost issue it is generally accepted that variations in medical practice and the cost of inpatient care suggest the possibility of inappropriate quality of care. This study is to closely examine the patterne and degrees of variation in cost structure of inpatient care among types of hospital and individual hospitals in some tracer diseases, and also to inquire into the service items which contribute much to the variation of total medical care cost. Foru common diseases, i.e. Cesarean Section, appendectomy, cataract extraction and pediatric pneumonia, were selected as tracer diseases. In most tracer diseases there were statistically significant differences in total medical care cost among hospitals in same type of hospital as well as among types of hospital(p<0.01). When total medical care cost were subdivided into the types of service, cost of medication and diagnostic examination varied the most prominenly. When the cost of medication were subdivided again, cost of parenteral antibiotics showed the most prominent variation. Of total medical care cost, medication was most contributory to the variation of total medical care cost(58.1~82.3%), and cost of antibiotics was most contributory to the variation of medication cost(63.9~92.2%). The results of study implicated that reducing the variation of medication may plays a significant role in containing the cost of inpatient care. In order to sort out the factors affecting practice variations including drug prescription pattes further researches are required.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.75-93
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• 2008

The rate of convergence of the distribution of order statistics to the corresponding extreme-value distribution may be characterized by the uniform and total variation metrics. de Haan and Resnick [4] derived the convergence rate when the second order generalized regularly varying function has second order derivatives. In this paper, based on the properties of the generalized regular variation and the second order generalized variation and characterized by uniform and total variation metrics, the convergence rates of the distribution of the largest order statistic are obtained under weaker conditions.

• Journal of Positioning, Navigation, and Timing
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• v.5 no.2
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• pp.87-96
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• 2016

The ionospheric error, which is one of many error elements considered during the Global Navigation Satellite System (GNSS) positioning, is hard to be predicted due to the influence of geomagnetic activity and irregular solar activities. Thus, the present study analyzed a change pattern in the ionosphere through Global Ionosphere Map (GIM) data for 12 years from 2003 to 2014 and a variation in the Slant Total Electron Content (STEC) between Sinuiju and Busan which was the longest range in the southeastern direction of the Korean Peninsula. The variation in the STEC verified the diurnal, annual, and solar cycle variations due to the influence of solar activity. The diurnal variation was characterized that the variation in the STEC started to increase from 6-7 am and reached the maximum at 13-14 pm followed by being decreased. The seasonal variation was characterized that the variation in the STEC was high in spring and autumn whereas it was low in summer and winter. The solar cycle variation revealed that the variation in the STEC increased during solar maximum and decreased during solar minimum. The variation in the STEC was up to 20 Total Electron Content Unit (TECU) during the solar minimum and up to 60 TECU during solar maximum.

• The Journal of the Korea Contents Association
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• v.6 no.4
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• pp.11-18
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• 2006

A new algorithm for removing salt and pepper impulse noise in image using impulse noise detector and total variation optimization is presented. The proposed two types of noise detectors which are based on the adaptive median filter, can detect impulse noise with high accuracy while reducing the probability of detecting image details as impulses. And the detectors maintain its performance independent of noise density. For removing impulses, total variation optimization is applied only to those detected noise candidate to reduces unnecessary computation. The proposed approach successfully remove impulse noise while preserving image details.

• Proceedings of the Korea Multimedia Society Conference
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• 2012.05a
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• pp.6-9
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• 2012

In this study, we compare two image denoising methods which are the Rudin-Osher-Fatemi total variation (TV) model and the nonlocal means (NLM) algorithm on medical images. To evaluate those methods, we used two well known measuring metrics. The methods are tested with a CT image, one X-Ray image, and three MRI images. Experimental result shows that the NML algorithm can give better results than the ROF TV model, but computational complexity is high.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.519-532
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• 2020

In this paper, we first propose a new total variation-based regularization model for image restoration. We next propose a fixed-point-like method for solving the new image restoration model, and then we provide convergence analysis for the fixed-point-like method. To evaluate the feasibility and efficiency of the fixed-point-like method for the new proposed total variation-based regularization model, we provide numerical experiments for several test problems.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.11
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• pp.4413-4425
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• 2020

In order to completely record all the information of realistic scenes, high dynamic range (HDR) images have been widely used in virtual reality, photography and computer graphics. A simple yet effective tone mapping method based on total variation is proposed so as to reproduce realistic scenes on low dynamic range (LDR) display devices. The structural component and texture component are obtained using total variation model in logarithmic domain. Then, the dynamic range of the structural component is compressed with an adaptive arcsine function. The texture component is processed by Taylor series. Finally, we adjust the saturation component using sigmoid function and restore the color information. Experimental results demonstrate that our method outperforms existing methods in terms of quality and speed.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.281-290
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• 2024

We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.