• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8 s.179
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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.

• The Journal of the Acoustical Society of Korea
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• v.19 no.4
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• pp.3-15
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• 2000

In this paper we present a new image denoising filter that can suppress additive noise components while preserving signal components in the wavelet domain. The proposed filter, which we call an adaptive wavelet shrinkage(AWS) filter, is composed of two operators: the wavelet killing operator and the adaptive shrinkage operator. Each operator is selected based on the threshold value which is estimated adaptively by using the local statistics of the wavelet coefficients. In the wavelet killing operation, the small wavelet coefficients below the threshold value are replaced by zero to suppress noise components in the wavelet domain. The adaptive shrinkage operator attenuates noise components from the wavelet components above the threshold value adaptively. The experimental results show that the proposed filter is more effective than the other methods in preserving signal components while suppressing noise.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.427-430
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• 2002

Recently the subject of "wavelet analysis" has be drawn by both mathematical and engineering application fields such as Signal Processing, Compression/Decomposition, Wavelet-Neural Network, Statistics and etc. Even though its similar to Fourier analysis, wavelet is a versatile tool with much mathematical content and great potential for applications. Especially, wavelet transform uses localizable various mother wavelet functions in time-frequency domain. Therefore, wavelet transform has good time-analysis ability for high frequency component, and has good frequency-analysis ability for low frequency component. Using the discriminative ability is more easy method than other conventional techniques. In this paper, Morlet wavelet transform was applied to discriminate the kind of line fault by acquired data from real power transformation network. The experimental result presented that Morlet wavelet transform is easier,and more useful method than the FFT (Fast Fourier Transform).

• Korean Journal of Remote Sensing
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• v.25 no.3
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• pp.215-223
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• 2009

The noise removal as a preprocessing was tried with various kinds of wavelet pairs. Wavelet transform for 2D images generally uses the same wavelets as basis functions in horizontal and vertical directions. A method with different wavelets was tried for each direction separately, which gives more precise interpretation of the classification. Total 486 pairs of wavelets from nine basis functions were tried to remove image noises. The classification accuracies before and after the noise removal were compared. Although all kinds of wavelet pairs showed the increased accuracies in classification, there were best and worst wavelet pairs depending on the data sets. Wavelet pairs with low energy percentage of LL band showed the high classification accuracy. A pattern was found in the results that very similar vertical accuracy was distributed for each horizontal ones. Since Haar is the shortest length filter, Haar could be a predictor wavelet to find the good wavelet pairs.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1387-1390
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• 1997

In this paper we propose a novel way to restore degraded image using wavelet transform & filterbank. First, we devide a degraded image into 4-suband images using UDWT(Undecimated Wavelet Transform), and then use a proper CLS (Constrained Least Square) filter in each subband. Using a proper CLS filter ineach subband, we can save high grequency components of original image. We reconstruct a restored image from the downsampled subband images using wavelet tansform. Even though there is a trade-off between ISNR and calculation loads, we reduce the calculation loads by using wavelet transform in reconstruction with a negligible degradatiion in ISNR.

• Proceedings of the IEEK Conference
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• 2001.06c
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• pp.15-168
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• 2001

In this paper, we propose growing algorithm of wavelet neural network. It is growing algorithm that adds hidden nodes using wavelet frame which approximately supports orthogonality in wavelet neural network based on wavelet theory. The result of this processing can be reduced global error and progresses performance efficiency of wavelet neural network. We apply the proposed algorithm to approximation problem and evaluate effectiveness of proposed algorithm.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.373-376
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• 2002

In this paper, we give the definition of the two dimensional q-Gabor wavelet. It consists of the q-normal distribution, which is also given in this paper. If the q-normal distribution is used as a kernel of the Gabor wavelet instead of the normal distribution, the q-Gabor wavelet is obtained. Furthermore, the q-Gabor wavelet is compared with the Gabor and the Haar wavelets to show how good The q-Gabor wavelet is.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.361-364
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• 1995

Wavelet Transform is a new tools for signal processing, such as data compressing extraction of parameter for Reconition and Diagnostics. This transform has an advandage of a good resolution compared to Fast Fourier Transform (FFT) In this study, we employ the wavelet transform for analysis of Acoustic Emission raw signal generated form rotary compressor. In abnormal condition of rotary compressor, the state of operating condition can be classified by analizing coefficient of wavelet transformed signal.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.39.3-39
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• 2001

Since Kalman filter and wavelet transform techniques are both suitable for a nonstationary process, wavelet-Kalman filter was proposed and applied to various industrial fields. However, the wavelet-Kalman filter subjected to model uncertainty with nonstationary process has not been considered. Thus, the robust wavelet-Kalman filter method is proposed in this paper. The proposed method can prevent the degradation of filter performance when parameter uncertainty exists in both the state and measurement matrices and preserve the merits of the standard Kalman filter in the sense that it produces optimal estimates. A simple example shows that the proposed approach outperforms the standard Kalman filter and the nominal wavelet-Kalman filter.

• Proceedings of the Korean Information Science Society Conference
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• 2001.10b
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• pp.472-474
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• 2001

본 논문은 wavelet 기반의 watershed를 이용한 효율적인 영상 분할을 기법을 제안한다. 영상 분할을 위해 입력 영상을 wavelet transform을 사용하여 low-resolution 영상을 생성한 후 watershed 알고리즘을 이용해 분할하고, 이를 Inverse wavelet transform함으로써 원 영상으로 복원한다. 복원된 영상을 의미 있는 영역들로 분할하기 위해 wavelet 특징값의 유사성을 두 인접한 영역에 비교하여 병합한다. 실험 결과 제안한 방법은 영상의 잡음에 대한 강인함과 영상의 과분할 문제를 해결할 수 있다.