• 한국멀티미디어학회논문지
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• 제8권6호
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• pp.776-782
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• 2005

This paper presents a SPIHT image compression method using biorthogonal multi wavelets on [-1,1]. A family of biorthogonal scaling vectors is constructed using fractal interpolation function, and the associated biorthogonal multi wavelets are constructed. This paper uses biorthogonal multi wavelets to be supported in [-1,1] associated with biorthogonal scaling vectors to be supported in [-1,1]. The scaling vectors and wavelets remain biorthogonal when restricted to integer intervals, making them well suited for bounded domains. The experiment results of simulation of the proposed image compression using biorthogonal multiwavelets on [-1,1] based on SPIHT were found to be excellent PSNR for LENA and PEPPERS images except for BABOON image than already existing single wavelets and DGHM multi wavelets.

• 대한수학회지
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• 제46권2호
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• pp.281-294
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• 2009

Accuracy of the scaling function is very crucial in wavelet theory, or correspondingly, in the study of wavelet filter banks. We are mainly interested in vector-valued filter banks having matrix factorization and indicate how to choose block central symmetric matrices to construct multi-wavelets with suitable accuracy.

• 대한전자공학회논문지SP
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• 제41권3호
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• pp.221-229
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• 2004

The Continuous Wavelets Transform project signal f(t) to "Time-scale"plan utilizing the time varied function which called "wavelets". This Transformation permit to analyze scale time dependence of signal f(t) thus the local or global scale properties can be extracted. Moreover, the signal f(t) can be reconstructed stably by utilizing the Inverse Continuous Wavelets Transform. In this paper, the EEG signal is analyzed by wavelets coherence method and the De-noising procedure is represented.

• 대한기계학회논문집A
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• 제24권8호
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• pp.2100-2107
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• 2000

The wavelet theory is relatively a new development and now acquires popularity and much interest in many areas including mathematics and engineering. This work presents an adaptive wavelet method for a numerical solution of partial differential equations in a collocation sense. Due to the multi-resolution nature of wavelets, an adaptive strategy can be easily realized it is easy to add or delete the wavelet coefficients as resolution levels progress. Typical wavelet-collocation methods use interpolating wavelets having no vanishing moment, but we propose a new wavelet-collocation method on modified interpolating wavelets having 2 vanishing moments. The use of the modified interpolating wavelets obtained by the lifting scheme requires a smaller number of wavelet coefficients as well as a smaller condition number of system matrices. The latter property makes a preconditioned conjugate gradient solver more useful for efficient analysis.

• 대한기계학회논문집A
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• 제24권8호
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• pp.2091-2099
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• 2000

The object of the present study is to present an adaptive wavelet-Galerkin method for the analysis of thin-walled box beam. Due to good localization properties of wavelets, wavelet methods emerge as alternative efficient solution methods to finite element methods. Most structural applications of wavelets thus far are limited in fixed-scale, non-adaptive frameworks, but this is not an appropriate use of wavelets. On the other hand, the present work appears the first attempt of an adaptive wavelet-based Galerkin method in structural problems. To handle boundary conditions, a fictitous domain method with penalty terms is employed. The limitation of the fictitious domain method is also addressed.

• 대한기계학회논문집B
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• 제28권12호
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• pp.1608-1615
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• 2004

CFD data compression methods based on Full-3D and Quasi-1D supercompact multiwavelets are presented. Supercompact wavelets method provide advantageous benefit that it allows higher order accurate representation with compact support. Therefore it avoids unnecessary interaction with remotely located data across singularities such as shock. Full-3D wavelets entails appropriate cross-derivative scaling function & wavelets, hence it can allow highly accurate multi-spatial data representation. Quasi-1D method adopt 1D multiresolution by alternating the directions rather than solving huge transformation matrix in Full-3D method. Hence efficient and relatively handy data processing can be conducted. Several numerical tests show swift data processing as well as high data compression ratio for CFD simulation data.

• 한국전자통신학회논문지
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• 제19권1호
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• pp.113-118
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• 2024

본 논문에서는 음향신호의 배경잡음을 소거하기 위한 시스템에서 최적의 wavelet을 제안한다. 이 시스템은 기존의 단구간 푸리에변환(STFT: Short Time Fourier Transform) 대신 이산 웨이블릿변환(DWT: Discrete Wavelet Transform)을 수행한 후 심층학습과정을 통하여 잡음소거 성능을 개선하였다. DWT는 다해상도 대역통과필터 기능을 하며 각 레벨에서 모 웨이블릿을 시간 이동시키고 크기를 스케일링한 여러 웨이블릿을 이용하여 변환 파라미터를 구한다. 여기서 음성을 분석하는데 가장 적합한 모(mother) 웨이블릿을 선정하기 위해 여러 웨이블릿에 대한 잡음소거 성능을 실험하였다. 본 연구에서 여러 웨이블릿에 대한 잡음소거시스템의 성능을 검증하기 위하여 Tensorflow와 Keras 라이브러리를 사용한 시뮬레이션 프로그램을 작성하고 가장 많이 사용되는 4개의 wavelet에 대해 모의실험을 수행하였다. 실험 결과, Haar 또는 Daubechies 웨이블릿을 사용하는 경우가 가장 우수한 잡음소거 성능을 나타냈으며 타 웨이블릿을 사용하는 경우보다 평균자승오차(MSE: Mean Square Error)가 크게 개선되는 것을 볼 수 있었다.

• 한국인터넷방송통신학회논문지
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• 제23권6호
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• pp.69-74
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• 2023

이 논문에서는 일차원과 이차원에서 불규칙한 점 집합에서의 웨이브렛을 구현하고 분석하는 기법이 기술되었다. 특히 우리는 부분할 방법과 계산에 집중하였다. 부분할은 선과 망사를 연속적인 분할 동작의 부드러운 곡선이나 곡선의 표면으로 간략화시키는 기법을 의미한다. 웨이브렛 구조를 특이한 환경에 일반화시키는 열쇠는 일반화된 부분할을 사용하는 것이다. 첫 번째 일반화 구조는 이미 부분할과 연결되었는데 그것은 이차 일반화 웨이브렛 구현에 보다 더 중요하게 되었다. 부분할 구조는 빠른 알고리즘을 제공하여주고, 자연적인 다해상도 구조를 만들어 주어 우리가 추구하려는 기본의 스케일 함수와 웨이브렛을 제공하여 준다.

• 대한전자공학회논문지SP
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• 제42권4호
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• pp.39-48
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• 2005

본 논문에서는 Bayesian 추정법과 신경회로망을 이용한 새로운 결 분할 방법을 제안한다 신경회로망의 입력으로는 다중스케일을 가지는 웨이블릿 계수와 인접한 이웃 웨이블릿 계수들의 문맥정보를 사용하고, 신경회로망의 출력을 사후 확률로 모델링한다. 문맥정보는 HMT(Hidden Markov Tree) 모델을 이용하여 구한다. 제안 방법은 HMT를 이용한 ML(Maximum Likelihood) 분할 보다 더 우수한 결과를 보여준다. 또한 HMT를 이용한 결 분할 방법과 제안 방법을 이용한 결 분할 각각에 HMTseg라고 불리는 다중 스케일 Bayesian 영상 분할 기술을 이용하여 후처리를 행한 결 분할 또한 제안 방법이 우수함을 보여준다.

• Journal of Mechanical Science and Technology
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• 제20권1호
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• pp.110-124
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• 2006

The multi scale wavelet-Galerkin method implemented in an adaptive manner has an advantage of obtaining accurate solutions with a substantially reduced number of interpolation points. The method is becoming popular, but its numerical efficiency still needs improvement. The objectives of this investigation are to present a new numerical scheme to improve the performance of the multi scale adaptive wavelet-Galerkin method and to give detailed implementation procedure. Specifically, the subdomain technique suitable for multiscale methods is developed and implemented. When the standard wavelet-Galerkin method is implemented without domain subdivision, the interaction between very long scale wavelets and very short scale wavelets leads to a poorly-sparse system matrix, which considerably worsens numerical efficiency for large-sized problems. The performance of the developed strategy is checked in terms of numerical costs such as the CPU time and memory size. Since the detailed implementation procedure including preprocessing and stiffness matrix construction is given, researchers having experiences in standard finite element implementation may be able to extend the multi scale method further or utilize some features of the multiscale method in their own applications.