• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.541-555
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• 1996

The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.

• Proceedings of the KOSOMBE Conference
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• v.1997 no.11
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• pp.172-175
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• 1997

Outline contour is detected firstly to simulate dose distribution in radiation therapy planning system. In this paper, we developed automatic contour detection system using temporal and spatial relationships of image sequences. The low level image analysis involves the use of directional gradient edge operators and Laplacian operator. The High level portion of algorithm uses a knowledge-based strategy that incorporates fuzzy resoning method.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2012.05a
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• pp.630-632
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• 2012

Contemporary society has evolved in the digital information age. Because of this, use of various digital images has been increased. To process these images, various digital image processing methods are used. Edge detection methods, one of those, are utilized to various areas of application such as object recognition, line detection. To detect edge, there are many methods such as Sobel, Prewitt, Laplacian. Because images which are dealt with existing methods are processed in same methods regardless the distribution of gray-level in image, edge detection property is insufficient. Therefore, In this study, to improve shortcomings of existing methods an algorithm using modified expansion mask is proposed.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2015.05a
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• pp.919-921
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• 2015

The edge is widely utilized as a preconditioning process in order to simplify the images in several fields such as the object recognition and detection. The edge detection methods which are generally known include the methods of Sobel, Roberts and Laplacian. However, such current methods have an advantage that the implementation is simple but bring more less an insufficient result since they use the fixed weighting mask. Therefore, an algorithm using the modified morphology is proposed in order to supplement such problems of the current edge detection methods and obtain the excellent edge detection, and also a simulation using this algorithm is conducted to compare with such current methods.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.81-105
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• 2003

This paper deals with the very interesting problem about the influence of piecewise smooth boundary conditions on the distribution of the eigenvalues of the negative Laplacian in R$^3$. The asymptotic expansion of the trace of the wave operator (equation omitted) for small ｜t｜ and i=√-1, where (equation omitted) are the eigenvalues of the negative Laplacian (equation omitted) in the (x$^1$, x$^2$, x$^3$)-space, is studied for an annular vibrating membrane $\Omega$ in R$^3$together with its smooth inner boundary surface S$_1$and its smooth outer boundary surface S$_2$. In the present paper, a finite number of Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components (equation omitted)(i = 1,...,m) of S$_1$and on the piecewise smooth components (equation omitted)(i = m +1,...,n) of S$_2$such that S$_1$= (equation omitted) and S$_2$= (equation omitted) are considered. The basic problem is to extract information on the geometry of the annular vibrating membrane $\Omega$ from complete knowledge of its eigenvalues by analysing the asymptotic expansions of the spectral function (equation omitted) for small ｜t｜.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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• pp.294-299
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• 2005

This paper presents the separation performance of the linearly mixed image signals with additive noises by using an independent component analyses(ICAs) of the fixed-point(FP) algorithm based on Newton and secant method, respectively. The Newton's FP-ICA uses the slope of objective function, and the secant's FP-ICA also uses the tangent line of objective function. The 2 kinds of ICA have been applied to the 2 dimensional 2-image with $512\times512$ pixels. Then Gaussian noise and Laplacian noise are added to the mixed images, respectively. The experimental results show that the Newton's FP-ICA has better the separation speed than secant FP-ICA and the secant's FP-ICA has also the better separation rate than Newton's FP-ICA. Especially, the Newton and secant method gives relatively larger improvement degree in separation speed and rate as the noise increases.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.8B
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• pp.1480-1489
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• 1999

In this paper, we propose a new post-processing method which can solve a problem of MSDS(Mean Squared Difference of Slope) method. Using that method the blocking artifacts can significantly be reduced without any restriction, which is a major drawback of block-based DCT compression method. In this approach, the OSLD(Overlapped Sub-Laplacian Distribution) of dequantized block boundary pixel difference values is defined and used to categorize each block of an image into one of four types. Those types are also classified into one of two classes: an edge and a non-edge classes. A slope across the block boundary is used to quantify discontinuity of the image. If an absolute estimated quantization error value of a DCT coefficient is greater than the corresponding quantization step size, it is saturated to the step size in the edge class. The proposed post-processing method can improve not only the PSNR value up to 0.1~O.3 dB but visual quality without any constraints determined by ad-hoc manner.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.1
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• pp.151-156
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• 2012

In this paper robust nonlinear image denoising algorithms are introduced for the distribution which is Gaussian in the center and Laplacian in the tails. The distribution is known as the least favorable ${\epsilon}$-contaminated normal distribution that maximizes the asymptotic variance. The proposed filter proves to be the maximum likelihood estimator under the heavy-tailed Gaussian noise environments. It is optimal in the respect of maximizing the efficacy under the above noise environment. Another filter for reducing impulsive noise is proposed by mixing with the myriad filter to propose an amplitude-limited myriad filter. Extensive experiment is conducted with images corrupted with ${\alpha}$-stable noise to analyze the behavior and performance of the proposed filters.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.6
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• pp.59-68
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• 2017

Random process plays a major role in wireless communication system to analytically derive the probability distribution function of the various statistical distribution. In this paper, we derive the decreasing function of the exponential distribution under the given condition which is expressed as wireless channel condition. The probability distribution function of Gaussian, Laplacian, Rayleigh and Nakagami distribution are also derived. Extensive simulation results of these statistical distributions are provided to prove that random process has a significant role in the wireless communications. In addition, the Rayleigh and Rician channels show specific examples of visible distance communication and invisible distance channel environment. This paper is motivated by that we assume a block fading channel model, where the channel is constant during a transmission block and changes independently between consecutive transmission block, can achieve a better performance in high SNR regime with i.i.d channel. This algorithm for realizing these transforms can be applied to the Kronecker MIMO channel.

• Journal of the Korean earth science society
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• v.38 no.2
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• pp.105-114
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• 2017

Two dimensional finite element method with quadrilateral basis functions was applied to the spherical high order filter on the spherical surface limited area domain. The basis function consists of four shape functions which are defined on separate four grid boxes sharing the same gridpoint. With the basis functions, the first order derivative was expressed as an algebraic equation associated with nine point stencil. As the theory depicts, the convergence rate of the error for the spherical Laplacian operator was found to be fourth order, while it was the second order for the spherical Laplacian operator. The accuracy of the new high order filter was shown to be almost the same as those of Fourier finite element high order filter. The two-dimension finite element high order filter was incorporated in the weather research and forecasting (WRF) model as a hyper viscosity. The effect of the high order filter was compared with the built-in viscosity scheme of the WRF model. It was revealed that the high order filter performed better than the built in viscosity scheme did in providing a sharper cutoff of small scale disturbances without affecting the large scale field. Simulation of the tropical cyclone track and intensity with the high order filter showed a forecast performance comparable to the built in viscosity scheme. However, the predicted amount and spatial distribution of the rainfall for the simulation with the high order filter was closer to the observed values than the case of built in viscosity scheme.