• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.367-375
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• 1996

Suppose the kernel function $\kappa$ belongs to $S(R^2)$ and is symmetric such that $ < \otimes x, \kappa >\geq 0$ for all $x \in S'(R)$. Let A be the class of functions f such that the function f is measurable on $S'(R)$ with $\int_{S'(R)}$\mid$f((I + tK)^{\frac{1}{2}}x$\mid$^2d\mu(x) < M$ for some $M > 0$ and for all t > 0, where K is the integral operator with kernel function $\kappa$. We show that the \lambda$-potential $G_Kf$ of f is a weak solution of $(\lambda I - \frac{1}{2} \tilde{\Xi}_{0,2}(\kappa))_u = f$.

• 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 Optical Society of Korea
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• v.12 no.3
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• pp.170-173
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• 2008

In this study, we simulated a statistical model of FCS(fluorescence correlation spectroscopy) based on a Poisson process to understand and explain observations of the experiment performed on molecules of ultra-low concentration by the home-built laser-scanning confocal microscope. The statistical model confirmed that the relative mean square amplitude of fluctuations is shown to be inversely proportional to the average number of molecules, even in the ultra-low concentration, if some conditions are satisfied. Signal-to-noise ratio and the variability of dwelling time under the confocal volume were found to be effective conditions for the experiment.

• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.4
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• pp.61-67
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• 2017

Low-dose X-ray fluoroscopic image sequences to avoid radiation exposure risk are contaminated by quantum noise. To restore these noisy sequences, we propose a 3D nonlocal means (NLM) filter based on stochastic distancesed can be applied to the denoising of X-ray fluoroscopic image sequences. The stochastic distance is obtained within motion-compensated noise filtering support to remove the Poisson noise. In this paper, motion-adaptive weight which reflected the frame similarity is proposed to restore the noisy sequences without motion artifact. Experimental results including comparisons with conventional algorithms for real X-ray fluoroscopic image sequences show the proposed algorithm has a good performance in both visual and quantitative criteria.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.559-574
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• 1998

Let the Gel'fand triple (E)$_{\beta}$/ ⊂ ( $L^2$) ⊂ (E)＊$_{\beta}$/ be the framework of white noise distribution theory constructed by Kon-dratiev and Streit. A new class of continuous multiplicative products on (E)$_{\beta}$/ is introduced and associated continuous derivations on (E)$_{\beta}$/ are discussed. Algebraic characterizations of first order differential operators on (E)$_{\beta}$/ are proved. Some applications are also discussed. $\beta$/ are proved. Some applications are also discussed.

• Proceedings of the IEEK Conference
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• 2006.06a
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• pp.391-392
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• 2006

In x-ray imaging system, twokinds of noises are involved. First, the charge generated from the radiation interaction with the detector during exposure is modeled by Poisson process. Second, the signal is then added by readout electronics noise, which is modeled by Gaussian distribution. In this paper, we applied Wiener filter and Wavelet to remove noise from medical X-ray image, the result shows that wavelet yield better segmentation results than the wiener filter.

• Journal of KSNVE
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• v.7 no.1
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• pp.127-134
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• 1997

The dynamic stability of classical plates and Mindlin plates subjected to pulsating follower forces is investigated in this paper. Using the finite element method, the induced equation is reduced to that of one with finite degrees of freedom. Then, the multiple scales method is applied to analyze the dynamic instability region. The effects of aspect ratio, Poisson ratio, rotary inertia and shear deformation on the dynamic stability of plates are studied in this paper.

• Applied Microscopy
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• v.48 no.4
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• pp.132-133
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• 2018

One of the most important factors determining the properties of a material is its grain size. However, unclear grain boundaries in the image hinder an accurate measurement of grain size. We demonstrate that grain boundaries existing in the images obtained by scanning transmission electron microscopy (STEM) can be clearly distinguished by applying a Sobel filter to a tilting series of STEM images of a hydrogenation-disproportionation-desorption-recombination processed Nd2Fe14B magnet sample.

• The KIPS Transactions:PartC
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• v.11C no.5
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• pp.621-632
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• 2004

Recent measurement studies of real teletraffic data in modern telecommunication networks have shown that self-similar (or fractal) processes may provide better models of teletraffic in modern telecommunication networks than Poisson processes. If this is not taken into account, it can lead to inaccurate conclusions about performance of telecommunication networks. Thus, an important requirement for conducting simulation studies of telecommunication networks is the ability to generate long synthetic stochastic self-similar sequences. A new generator of pseu-do-random self-similar sequences, based on the fractional Gaussian nois and a wavelet transform, is proposed and analysed in this paper. Specifically, this generator uses Daubechies wavelets. The motivation behind this selection of wavelets is that Daubechies wavelets lead to more accurate results by better matching the self-similar structure of long range dependent processes, than other types of wavelets. The statistical accuracy and time required to produce sequences of a given (long) length are experimentally studied. This generator shows a high level of accuracy of the output data (in the sense of the Hurst parameter) and is fast. Its theoretical algorithmic complexity is 0(n).

• Genomics & Informatics
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• v.19 no.3
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• pp.34.1-34.6
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• 2021

Digital PCR (dPCR) is the third-generation PCR that enables real-time absolute quantification without reference materials. Recently, global diagnosis companies have developed new dPCR equipment. In line with the development, the Lab On An Array (LOAA) dPCR analyzer (Optolane) was launched last year. The LOAA dPCR is a semiconductor chip-based separation PCR type equipment. The LOAA dPCR includes Micro Electro Mechanical System that can be injected by partitioning the target gene into 56 to 20,000 wells. The amount of target gene per wells is digitized to 0 or 1 as the number of well gradually increases to 20,000 wells because its principle follows Poisson distribution, which allows the LOAA dPCR to perform precise absolute quantification. LOAA determined region of interest first prior to dPCR operation. To exclude invalid wells for the quantification, the LOAA dPCR has applied various filtering methods using brightness, slope, baseline, and noise filters. As the coronavirus disease 2019 has now spread around the world, needs for diagnostic equipment of point of care testing (POCT) are increasing. The LOAA dPCR is expected to be suitable for POCT diagnosis due to its compact size and high accuracy. Here, we describe the quantitative principle of the LOAA dPCR and suggest that it can be applied to various fields.