• IEIE Transactions on Smart Processing and Computing
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• v.5 no.6
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• pp.403-417
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• 2016

This paper reviews recent published works dealing with the application of wavelets to image processing based on multiresolution analysis. After revisiting the basics of wavelet transform theory, various applications of wavelets and multiresolution analysis are reviewed, including image denoising, image enhancement, super-resolution, and image compression. In addition, we introduce the concept and theory of quaternion wavelets for the future advancement of wavelet transform and quaternion multiresolution applications.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.9
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• pp.827-833
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• 2013

In this paper, an efficient computational method is presented for state space analysis of bilinear systems via Legendre wavelets. The differential matrix equation is converted to a generalized Sylvester matrix equation by using Legendre wavelets as a basis. First, an explicit expression for the inverse of the integral operational matrix of the Legendre wavelets is presented. Then using it, we propose a preorder traversal algorithm to solve the generalized Sylvester matrix equation, which greatly reduces the computation time. Finally the efficiency of the proposed method is discussed using numerical examples.

• 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.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.561-570
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• 2012

Fourier transform is well known for trigonometric systems. It is also a very useful tool for the construction of wavelets. The method of constructing wavelets has evolved as times went by. We review some methods. Then we do some calculations on wavelets defined by its Fourier transform.

• Textile Coloration and Finishing
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• v.18 no.5 s.90
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• pp.88-93
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• 2006

A data compression system has been developed by combining adaptive wavelets and optimization technique. The adaptive wavelets were made by optimizing the coefficients of the wavelet matrix. The optimization procedure has been performed by criteria of minimizing the reconstruction error. The resulting adaptive basis outperformed such conventional basis as Daubechies-5 by 5-10%. It was also shown that the yarn density profiles could be compressed by over 95% without a significant loss of information.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.507-517
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• 2000

Existence of Gibbs' phenomenon has been well known in wavelet expansions. But the estimation of its size is another problem. Because of the oscillation of wavelets, it is not easy to estimate the Gibbs size of wavelet expansions. For wavelets defined via Fourier transforms, we give a new formula to calculate the size of overshoot. But using this we compute the size of Gibbs effect for Barttle-Lemarier wavelets.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.267-275
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• 2004

While the convergence of the classical Fourier series has been well known, the rate of its convergence is not well acknowledged. The results regarding the rate of convergence of the Fourier series and wavelet expansions can be found in the book of Walter[5]. In this paper, we give the rate of convergence of hybrid sampling series associated with orthogonal wavelets.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.181-189
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• 2017

A method for recovering Chui-Lian's orthogonal symmetric/antisymmetric multiwavelets of order 2 from orthogonal two-direction wavelets of order 2 was proposed by Yang and Xie. In this paper we pursue the converse, that is, we propose a method for constructing orthogonal two-direction wavelets of order 2 from orthogonal symmetric/antisymmetric multiwavelets of order 2.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.613-620
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• 2004

The concept of Gibbs’ phenomenon has not been made for higher dimension in wavelets. In this paper we extend the concept in two dimensional wavelets. We give the fundamental concept of jump discontinuity in two dimensions. We provide the criteria for the existence of Gibbs phenomenon for both separable and tensor product wavelets.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.17-30
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• 2007

A new scheme for solving the Vlasov equation using a compactly supported wavelets basis is proposed. We use a numerical method which minimizes the numerical diffusion and conserves a reasonable time computing cost. So we introduce a representation in a compactly supported wavelet of the derivative operator. This method makes easy and simple the computation of the coefficients of the matrix representing the operator. This allows us to solve the two equations which result from the splitting technique of the main Vlasov equation. Some numerical results are exposed using different numbers of wavelets.