• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.423-431
• /
• 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.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.22 no.7
• /
• pp.1515-1522
• /
• 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.

• Journal of Korea Multimedia Society
• /
• v.8 no.1
• /
• pp.19-26
• /
• 2005

The basis function of wavelet transform used in this paper is constructed by using lifting scheme, which is different from general wavelet transform. Lifting scheme is a new biorthogonal wavelet con-structing method, that does not use Fourier transform for constructing its basis function. In this paper, an image compression and reconstruction method using the lifting scheme was proposed. And this method improves data visualization by supporting a partial reconstruction and a local reconstruction. Approx- imations at various resolutions allow extracting various sizes of feature from an image or signal with a small amount of original information. An approximation with small size of scaling coefficients gives a brief outline of features at fast. Image compression and edge detection techniques provide good frame- works for data management and visualization in multimedia database.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.49 no.9
• /
• pp.425-432
• /
• 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.