• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.305-334
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• 2005

The objective of this study is to analyze the decay characteristics of the hat interpolation wavelet coefficients of some smooth functions defined in a two-dimensional space. The motivation of this research is to establish some fundamental mathematical foundations needed in justifying the adaptive multiresolution analysis of the hat-interpolation wavelet-Galerkin method. Though the hat-interpolation wavelet-Galerkin method has been successful in some classes of problems, no complete error analysis has been given yet. As an effort towards this direction, we give estimates on the decaying ratios of the wavelet coefficients at children interpolation points to the wavelet coefficient at the parent interpolation point. We also give an estimate for the difference between non-adaptively and adaptively interpolated representations.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.265-270
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• 2007

The modern approach for wavelets imposes a Bayesian prior model on the wavelet coefficients to capture the sparseness of the wavelet expansion. The idea is to build flexible probability models for the marginal posterior densities of the wavelet coefficients. In this note, we derive exact expressions for a popular model for the marginal posterior density.

• Proceedings of the IEEK Conference
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• summer
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• pp.244-248
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• 2004

This paper proposes a new noise cancellation method for speech recognition in noise environments. We determine the time adaptive threshold value using standard deviations of wavelet coefficients after wavelet transform by frames. The time adaptive threshold value is set up by using sum of standard deviations of wavelet coefficients in cA3 and weighted cD1. cA3 coefficients represent the voiced sound with lower frequency components and cD1 coefficients represent the unvoiced sound with higher frequency components. In experiments, we removed noise after adding white Gaussian noise and colored noise to original speech. The proposed method improved SNR and MSE more than wavelet transform and wavelet packet transform does. As a result of speech recognition experiment using noise speech DB, recognition performance is improved by $2\sim4\;\%.$

• Proceedings of the IEEK Conference
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• 2008.06a
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• pp.821-822
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• 2008

This paper presents a new demosaicking method based on weighted sum in the wavelet domain. In our method, the missing wavelet coefficients in lowest frequency subband are obtained by weighted sum. Since detail coefficients have large values at the edge region, these values are used as weighting factors. Detail coefficients are replaced by the coefficients in the corresponding subbands. Experimental results show that the proposed method generates good performance.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.3
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• pp.493-505
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• 1997

In this paper, a wavelet image compression method using human visually estimated quantizer is proposed. The quantizer has three components. These are constructed by using effects of frequency band, background luminance, and spatial masking. The first quantization factor is a fixed constant value for each band. The second factor is calculated by averaging four wavelet coefficients in the lowest frequency band. The third factor is determined by the difference between wavelet coefficients in the lowest frequency band. Arithmetic coding is used for encoding quantized wavelet coefficients. Coefficients in the lowest band are transmitted without loss. Therefore the compressed image is decompressed by using three quantization factors which can be calculated in the receiver. Compared with previous image compression methods which adopted human visual system, the proposed method shows improved results with less computational cost.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.7-12
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• 2009

In JPEG2000, the Cohen-Daubechies-Feauveau (CDF) 9/7-tap wavelet filter adopted in lossy compression is implemented by the lifting scheme or by the convolution scheme while the LeGall 5/3-tap wavelet filter adopted in lossless compression is implemented just by the lifting scheme. However, these filters are not optimal in terms of Peak Signal-to-Noise Ratio (PSNR) values, and irrational coefficients of wavelet filters are complicated. In this paper, we proposed a method to optimize image quality based on wavelet filter design and on wavelet decomposition. First, we propose a design of wavelet filters by selecting the most appropriate rational coefficients of wavelet filters. These filters are shown to have better performance than previous wavelet ones. Then, we choose the most appropriate wavelet decomposition to get the optimal PSNR values of images.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.149-152
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• 2000

This paper addresses the wavelet fuzzy modeling using Virus-Evolutionary Genetic Algorithm (VEGA). We build a fuzzy system model which is equivalent to the wavelet transform after identifying the coefficients of wavelet transform. We can obtain an accurate system model with a small number of coefficients due to the energy compaction property of the wavelet transform. It thus means that we can construct a fuzzy system model with a small number of rules. In order to identify the wide-ranged coefficients of the wavelet transform, VEGA is adopted, which has prominent ability to avoid premature local convergence that is suitable to complex optimization problems. We demonstrate the superiority of our proposed fuzzy system modeling method over the previous results by modeling nonlinear function.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.429-436
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• 2004

For the in-situ health monitoring of critical members in civil infra-structures, ultrasonic guided Lamb waves-based non-destructive evaluation (NDE) is very suitable. However, a chief drawback of the Lamb wave techniques is that multiple modes exist at all frequencies and the modes are generally dispersive, which means that the received signals may be very complicated. To overcome these complications, selective transmitting and receiving of a single A/sub 0/ mode within a frequency range can be adopted. Furthermore, a wavelet technique can be utilized to decompose the Lamb wave response into wavelet coefficients as a tool for signal processing. The changes in the Lamb waves interacting with damages in the steel plates are successfully characterized by this wavelet technique, through the amplitude change of the wavelet coefficients. In this paper, the feasibility of detecting a line crack on the surface of a steel plate and loosened bolts in a joint steel specimen using the Lamb waves and the wavelet technique is investigated.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.635-637
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• 1998

Based on wavelet theory, the new notion of wavelet networks is proposed as alternative to feedforward neural networks for approximating arbitrary nonlinear functions. An algorithm presented in this paper trains coefficients of wavelet. i.e., translations and scaling., and then learns weights with the wavelet coefficients. And experimental results are reported.

• Journal of Broadcast Engineering
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• v.2 no.1
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• pp.65-73
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• 1997

This paper propose a new triangular mesh approximation method using wavelet coefficients for large terrain data. Using spatio-freguency localization characteristics of wavelet coefficients, we determine the complexity of terrain data and approximate the data according to the complexity. This proposed algorithm is simple and requires low computational cost due to its top-down approach. Because of the similarity between the mesh approximation and data compression procedures based on wavelet transform, we combine the mesh approximation scheme with the Embedded Zerotree Wavelet (EZW) coding scheme for the effective management of large terrain data. Computer simulation results demonstrate that the proposed algorithm is very prospective for the 3-D visualization of terrain data.