• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.279-294
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• 2013

We are interested in an adaptive grid method for hyperbolic equations. A multiresolution analysis, based on a biorthogonal family of interpolating scaling functions and lifted interpolating wavelets, is used to dynamically adapt grid points according to the physical field profile in each time step. Traditional finite-difference schemes with fixed stencils produce high oscillations around sharp discontinuities. In this paper, we hybridize high-resolution schemes, which are suitable for capturing singularities, and apply a finite-difference approach to the scaling functions at non-singular points. We use a total variation diminishing Runge-Kutta method for the time integration. The computational cost is proportional to the number of points present after compression. We provide several numerical examples to verify our approach.

• Environmental Engineering Research
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• v.10 no.2
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• pp.88-103
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• 2005

In this paper, data-driven modeling and multiresolution analysis (MRA) are applied for a full-scale wastewater treatment plant (WWTP). The proposed method is based on modeling by partial least squares (PLS) and multiscale monitoring by a generic dissimilarity measure (GDM), which is suitable for nonstationary and non-normal process monitoring such as a biological process. Case study in an industrial plant showed that the PLS model could give good modeling performance and analyze the dynamics of a complex plant and MRA was useful to detect and isolate various faults due to its multiscale nature. The proposed method enables us to show the underlying phenomena as well as to filter out unwanted and disturbing phenomena.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.285-308
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• 2000

We generalize bi-orthogonal (non-orthogona) MRA to frame MRA in which the family of integer translates of a scaling func-tion forms a frame for the initial ladder space V0. We investigate the internal structure of frame MRA and establish the existence of a dual scaling function, and show that, unlike bi-orthogonal MRA, there ex-ists a frame MRA that has no (frame) 'wavelet'. Then we prove the existence of a dual wavelet under the assumption of the existence of a wavelet and present easy sufficient conditions for the existence of a wavelet. Finally we give a new proof of an equivalent condition for the translates of a function in L2(R) to be a frame of its closed linear span.

• Journal of the Korean Institute of Telematics and Electronics T
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• v.35T no.3
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• pp.37-45
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• 1998

In this paper, the different frequency component and time informations from an EMI signal are extracted simultaneously using a wavelet transform and the results of transform in the time and frequency domain are analyzed. Frequencies are extracted from the EMI signal by performing the multiresolution analysis using the Daubechies-4 filter coefficients and the time information through the results of wavelet transform. We have tried the correlation analysis to evaluate the results of wavelet transform. We have chosen the optimal wavelet function for an object signal by comparing the transformed results of various wavelet functions and verified the simulation examples of waveform and harmonic analysis using a wavelet transform. We have proved the denoising effect to the EMI signal using the soft thresholding technique.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.15 no.1
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• pp.84-89
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• 2001

This paper deals with multiresolution analysis of wavelet transform for partial discharge(PD), composite discharge(corona + surlace discharge). Multiresolution analysis was used for performing discrete wavelet transform PD signals was decomposed into "approximation" and "detail" cOmpJnents until 4 levels by using discrete wavelet analysis. In this paper, daubechies family is adopted for the research of the characteristics of PD signals. 1be results show that in corona discharge the segment 7, 8, 9, 10, 1] values of defined variable is increased with discharge process, so phase distribution is characterized by 210~330 ranges. In case surface discharge in expoxy insulator inserted, defined variable values is fairly symmetric chscharge pattern because coupled both corona and dielectric oounded discharges. We can confimJly discriminate the type of PD source.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2014.06a
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• pp.226-229
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• 2014

본 논문은 효과적인 열화영상의 복원을 위해 Multiresolution Bilateral Filter (MBF) 기반의 구간적 노이즈 분석을 제안한다. 기존의 MBF 알고리즘은 최적화되지 않은 노이즈 추정 값을 중첩적으로 사용하다보니 over smoothing 현상이 발생되는 결과가 도출되기도 하였다. 이에 따른 보완점으로 열화영상 내 전체 화소를 일정한 블록 단위의 영역으로 나누어, 영상특성을 최대한 보존하며 노이즈제거를 진행하기 위해 블록 단위의 영역 내에서 노이즈 추정을 위한 파라미터를 추가한다. 실험을 통해 제안된 알고리즘이 노이즈 추정을 수행하여 얻어진 노이즈의 분산 값을 보다 정확히 추정하였고, 이로 인하여 향상된 노이즈 제거 영상 획득이 가능함을 확인할 수 있었다.

• Journal of information and communication convergence engineering
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• v.5 no.1
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• pp.1-6
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• 2007

In the process of the acquisition, storage, transmission of signals, noises are generated by various causes and the degradation phenomenon by noises tends to generate serious errors for the signal with information. So, in order to analyze and remove these noises, studies on numerous mathematical methods such as the Fourier transform have been implemented. And recently there have been many ongoing wavelet-based denoising algorithms representing excellent characteristics in time-frequency localization and multiresolution analysis, but the method to remove additive white Gaussian noise (AWGN) and the impulse noise simultaneously was not given. So, to reconstruct the corrupted signal by noises, in this paper a novel wavelet-based denoising algorithm was proposed and using signal-to-noise ratio (SNR) this method was compared to conventional methods.

• Korean Journal of Remote Sensing
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• v.20 no.3
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• pp.207-214
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• 2004

This study focused on providing a methodology to utilize temporal information obtained from remotely sensed data for monitoring a wide variety of targets on the earth's surface. Generally, a methodology in understanding of global changes is composed of mapping, quantifying, and monitoring changes in the physical characteristics of land cover. The selected processing and analysis technique affects the quality of the obtained information. In this research, feature extraction methodology is proposed based on segmentation. It requires a series of processing of multitempotal images: preprocessing of geometric and radiometric correction, image subtraction/thresholding technique, and segmentation/thresholding. It results in the mapping of the change-detected areas. Here, the appropriate methods are studied for each step and especially, in segmentation process, a method to delineate the exact boundaries of features is investigated in multiresolution framework to reduce computational complexity for multitemporal images of large size.

• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.293-300
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• 2011

In this paper, we obtain that the space $\mathcal{W}_2$ of minimally supported frequency wavelets, the supports of whose Fourier transforms consist of two intervals, is path-connected.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.4
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• pp.758-763
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• 2006

In various fields of basic science and engineering, in order to present signals and systems exactly and acquire useful information from spatial and timely changes, many researches have been processed. In these methods, the Fourier transform which represents signal as the combination of the frequency component has been applied to the most fields. But as transform not to consider time information, the Fourier transform has its limitations of application. To overcome this problem, a variety of methods including the wavelet transform have been proposed. As transform to represent signal by using the changing window, according to scale parameter in time-scale domain, the wavelet transform is capable of multiresolution analysis and defines various functions according to the application environments. In this paper, to detect features of signal we analyzed wavelet the spectrum by using the basis function of the fourier transform.