• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.3
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• pp.221-229
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• 2004

The Continuous Wavelets Transform project signal f(t) to "Time-scale"plan utilizing the time varied function which called "wavelets". This Transformation permit to analyze scale time dependence of signal f(t) thus the local or global scale properties can be extracted. Moreover, the signal f(t) can be reconstructed stably by utilizing the Inverse Continuous Wavelets Transform. In this paper, the EEG signal is analyzed by wavelets coherence method and the De-noising procedure is represented.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.289-305
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• 1998

We consider unimodular wavelets and scalling functions whose Fourier transforms are supported in a finite disjoint uniof of closed intervals. In particular, we characterize those unimodular wavelets which can be associated with multiresolution analysis. As an application we have a criterion to determine whether a wavelet from a class of unimodular wavelets of Ha et al. can be associated with multiresolution analysis or not.

• Journal of the Korean Data and Information Science Society
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• v.15 no.3
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• pp.695-706
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• 2004

The use of wavelets in three-dimensional imaging is reviewed with an example. The insufficiencies of direct two-dimensional processing is showed as a major motivating factor behind using wavelets for three-dimensional imaging. Different wavelet algorithms are used, and these are compared with the direct two-dimensional approach as well as with each other.

• Journal of Korea Multimedia Society
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• v.8 no.6
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• pp.776-782
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• 2005

This paper presents a SPIHT image compression method using biorthogonal multi wavelets on [-1,1]. A family of biorthogonal scaling vectors is constructed using fractal interpolation function, and the associated biorthogonal multi wavelets are constructed. This paper uses biorthogonal multi wavelets to be supported in [-1,1] associated with biorthogonal scaling vectors to be supported in [-1,1]. The scaling vectors and wavelets remain biorthogonal when restricted to integer intervals, making them well suited for bounded domains. The experiment results of simulation of the proposed image compression using biorthogonal multiwavelets on [-1,1] based on SPIHT were found to be excellent PSNR for LENA and PEPPERS images except for BABOON image than already existing single wavelets and DGHM multi wavelets.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.649-671
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• 2020

In this paper we give the harmonic analysis associated with the Cherednik operators, next we define and study the Cherednik wavelets and the Cherednik windowed transforms on ℝd, in the W-invariant case, and we prove for these transforms Plancherel and inversion formulas. As application we give these results for the Gaussian Cherednik wavelets and the Gaussian Cherednik windowed transform on ℝd in the W-invariant case.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.281-294
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• 2009

Accuracy of the scaling function is very crucial in wavelet theory, or correspondingly, in the study of wavelet filter banks. We are mainly interested in vector-valued filter banks having matrix factorization and indicate how to choose block central symmetric matrices to construct multi-wavelets with suitable accuracy.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.411-418
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• 2005

We review support vector and wavelet density estimation. The relationship between support vector and wavelet density estimation in reproducing kernel Hilbert space (RKHS) is investigated in order to use wavelets as a variety of support vector kernels in support vector density estimation.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.46-49
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• 2003

A concept of fuzzy wavelets is proposed by a fuzzification of morphological wavelets. In the proposed fuzzy wavelets, analysis and synthesis schemes can be formulated as the operations of fuzzy relational calculus. In order to perform an efficient compression and reconstruction, an alphaband is also proposed as a soft thresholding of the wavelets. In the image compression/reconstruction experiment using test images extracted Standard Image DataBAse (SIDBA), it is confirmed that the root mean square error (RMSE) of the proposed soft thresholding is decreased to 87.3％ of the conventional hard thresholding.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1069-1096
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• 2015

In this article we introduce a numerical method, named Gegenbauer wavelets method, which is derived from conventional Gegenbauer polynomials, for solving fractional initial and boundary value problems. The operational matrices are derived and utilized to reduce the linear fractional differential equation to a system of algebraic equations. We perform the convergence analysis for the Gegenbauer wavelets method. We also combine Gegenbauer wavelets operational matrix method with quasilinearization technique for solving fractional nonlinear differential equation. Quasilinearization technique is used to discretize the nonlinear fractional ordinary differential equation and then the Gegenbauer wavelet method is applied to discretized fractional ordinary differential equations. In each iteration of quasilinearization technique, solution is updated by the Gegenbauer wavelet method. Numerical examples are provided to illustrate the efficiency and accuracy of the methods.

• Journal of Electrical Engineering and information Science
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• v.3 no.3
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• pp.348-354
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• 1998

The measured equation of invariance (MEI) method was introduced as a way to determine the electromagnetic fields scattered from discrete objects. Unlike more traditional numerical methods, MEI method over conventional methods over conventional methods are very substantial. In this work, Haar wavelets are applied to the measured equation of invariance (MEI) to solve two-dimensional scattering problem. We refer to "MEI method with wavelets" as "Wavelet MEI method". The proposed method leads to a significant saving in the CPU time compared to the MEI method that does not use wavelets as metrons. The results presented in this work promise that the Wavelet MEI method can give an accurate result quickly. We believe it is the first time that wavelets have been applied in conjunction with the MEI method to solve this scattering problem.