• 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.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.859-866
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• 2001

The problem of wavelet density estimation is studied when the sample observations are contaminated with random noise. In this paper a linear wavelet estimator based on Meyer-type wavelets is shown to be L$_1$ strongly consistent for f(x) with bounded support when Fourier transform of random noise has polynomial descent or exponential descent.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.409-412
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• 2003

In this paper, the encoder architecture of 3-D wavelet transform based on lifting scheme is designed. Architecture, here, 3 level wavelet transform for spatial decomposition and 2 level wavelet transform for temporal decomposition is adopted with efficient computation.

• Journal of applied mathematics & informatics
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• v.9 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.639-647
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• 1996

• Sleep Medicine and Psychophysiology
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• v.19 no.1
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• pp.11-17
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• 2012

Objective: Among various methods developed to quantitatively explore electroencephalograms (EEG), we focused on a wavelet method that was known to yield robust results under nonstationary conditions. The aim of this study was thus to introduce the wavelet method and demonstrate its potential use in clinical sleep studies. Method: This study involved artificial EEG specifically designed to validate the wavelet method. The method was performed to obtain time-dependent spectral power and phase angles of the signal. Synchrony of multichannel EEG was analyzed by an order parameter of the instantaneous phase. The standard methods, such as Fourier transformation and coherence, were also performed and compared with the wavelet method. The method was further validated with clinical EEG and ERP samples available as pilot studies at academic sleep centers. Result: The time-frequency plot and phase synchrony level obtained by the wavelet method clearly showed dynamic changes in the EEG waveforms artificially fabricated. When applied to clinical samples, the method successfully detected changes in spectral power across the sleep onset period and identified differences between the target and background ERP. Conclusion: Our results suggest that the wavelet method could be an alternative and/or complementary tool to the conventional Fourier method in quantifying and identifying EEG and ERP biomarkers robustly, especially when the signals were nonstationary in a short time scale (1-100 seconds).

• The Journal of the Korea institute of electronic communication sciences
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• v.4 no.3
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• pp.190-196
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• 2009

A new time adapted threshold using the standard deviations of Wavelet coefficients after Wavelet transform by frame scale is proposed. The time adapted threshold is set up using the sum of standard deviations of Wavelet coefficient in level 3 approximation and weighted level 1 detail. Level 3 approximation coefficients represent the voiced sound with low frequency and level 1 detail coefficients represent the unvoiced sound with high frequency. After reducing noise by soft thresholding with the proposed time adapted threshold, there are still residual noises in silent interval. To reduce residual noises in silent interval, a detection algorithm of silent interval is proposed. From simulation results, it can be noticed that SNR and MSE of the proposed algorithm are improved than those of Wavelet transform and than those of Wavelet packet transform.

• Architectural research
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• v.11 no.1
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• pp.7-14
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• 2009

In this paper, we take advantage of Wavelet Transform to identify damping ratios of membrane structures under wind action. Due to the lightweight and flexibility of membrane structures, they are very sensitive to the wind load, and show a type of fluid-structure interaction phenomenon simultaneously. In this study, we firstly obtain the responses of an air-supported membrane structure by ADINA with the consideration of this characteristic, and then conduct Wavelet Transform on these responses. Based on the Wavelet Transform, damping ratios could be obtained from the slope of Wavelet Transform in a semi-logarithmic scale at a certain dilation coefficient. According to this principle, damping ratios could eventually be obtained. There are two numerical examples in this study. The first one is a simulated signal, which is used to verify the accuracy of the Wavelet Transform method. The second one is an air-supported membrane structure under wind action, damping ratios obtained from this method is about 0.05~0.09. The Wavelet Transform method could be regarded as a very good method for the the damping analysis, especially for the large spatial structures whose natural frequencies are closely spaced.

• Proceedings of the Korea Contents Association Conference
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• 2003.05a
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• pp.376-382
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• 2003

Recently, there have been many types of wavelet transformations proposed to remove the noise from an signal and image data By using feature of seperating the noise from the original image the Wavelet transformations can retain the edges of the images The wavelet analysis is complete when the basis function is coded into the wavelet This Thesis describes a method of using wavelet transformation to remove the noise from an image signal. Although the wavelet transformation proposed by Donoho and Johnstone works, it does not reliably remove all the noise from the images. So this thesis propose an algorithm that selected Wavelet Shrinkgae and threshold according to the features of bands and amplitude of noise.

• Journal of Advanced Navigation Technology
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• v.20 no.6
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• pp.539-543
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• 2016

In this paper, we study the technique to improve the performance of the aerial images taken by UAV using daubechies stationary wavelet transform. When aerial images taken by UAV were damaged by gaussian noise very commonly applied, the experiment for image performance improvement was performed. It was known that stationary wavelet transform is the transferring solution to the problem occurred by down sampling from DWT also more efficient to remove noise than DWT. Also haar wavelet is discontinuous function so not efficient for smooth signal and image processing. Therefore, this study is confirmed that the noise can be removed by daubechies stationary wavelet and the performance is improved by haar stationary wavelet.