• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.423-431
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• 2002

In this paper, we find $n^{th}$ order wavelet derivatives of a sufficiently smooth function using biorthogonal wavelet bases and derive the order of convergence of the $n^{th}$ order wavelet derivatives.

• 한국통신학회논문지
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• 제22권7호
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• pp.1515-1522
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• 1997

Several image coding algorithms have been developed for the telecommunication and multimedia systems with high image quality and high compression ratio. In order to achieve low entropy and distortion, the system should pay great cost of computation time and memory. In this paper, the uniform cubic lattice is chosen for Lattice Vector Quantization (LVQ) because of its generic simplicity. As a transform coding, the Discrete Wavelet Transform (DWT) is applied to the images because of its multiresolution property. The proposed algorithm is basically composed of the biorthogonal DWT and the uniform cubic LVQ. The multiresolution property of the DWT is actively used to optimize the entropy and the distortion on the basis of the distortion-rate function. The vector codebooks are also designed to be optimal at each subimage which is analyzed by the biorthogonal DWT. For compression efficiency, the vector codebook has different dimension depending on the variance of subimage. The simulation results show that the performance of the proposed coding mdthod is superior to the others in terms of the computation complexity and the PSNR in the range of entropy below 0.25 bpp.

• 한국멀티미디어학회논문지
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• 제8권1호
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• pp.19-26
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• 2005

본 논문에서 사용한 웨이블릿 변환의 기저 함수는 일반적인 웨이블릿 변환과 다른 리프팅 스킴을 사용하여 만들어 졌다. 리프팅 스킴은 푸리에 변환을 사용하여 기저 함수를 생성하지 않는 새로운 쌍직교 웨이블릿 기저 함수를 생성하는 방법이다 본 본문은 리프팅 스킴을 이용한 새로운 영상 압축 및 에지 검출 방법을 제안하고 있다. 그리고 이 방법은 부분 복원과 공간 복원을 할 수 있어 데이터 가시화를 향상시킬 수 있다. 다양한 해상도에서의 근사 영상은 원래 영상으로부터 적은 정보만으로 다양한 크기의 특징을 뽑아낼 수 있고, 적은 양의 스케일링 계수를 사용하여 생성된 근사 영상은 빠르게 원래 영상의 대략적인 개요만이 필요할 때 유용하게 사용된다. 본 논문에서 제안한 영상 압축 및 에지 검출 기법은 멀티미디어 데이터베이스에서 데이터 관리와 데이터 가시화를 향상시킬 수 있는 좋은 기틀을 마련해 준다.

• 대한전기학회논문지:전력기술부문A
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• 제49권9호
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• pp.425-432
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• 2000

Wavelet transform is a new method fro electric power quality analysis. Several types of mother wavelets are compared using voltage sag data. Investigations on the use of some mother wavelets, namely Daubechies, Symlets, Coiflets, Biorthogonal, are carried out. On the basis of extensive investigations, optimal mother wavelets for the detection of voltage sag are chosen. The recommended mother wavelet is 'Daubechies 4(db4)' wavelet. 'db4', the most commonly applied mother wavelet in the power quality analysis, can be used most properly in disturbance phenomena which occurs rapidly for a short time. This paper presents a discrete wavelet transform approach for determining the beginning time and end time of voltage sags. The technique is based on utilising the maximum value of d1(at scale 1) coefficients in multiresolution analysis(MRA) based on the discrete wavelet transform. The procedure is fully described, and the results are compared with other methods for determining voltage sag duration, such as the RMS voltage and STFT(Short-Time Fourier Transform) methods. As a result, the voltage sag detection using wavelet transform appears to be a reliable method for detecting and measuring voltage sags in power quality disturbance analysis.