• Title, Summary, Keyword: wavelets

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UNIMODULAR WAVELETS AND SCALING FUNCTIONS

  • Kim, Hong-Oh;Park, Jong-Ha
    • 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.

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EEG Signal Compression by Multi-scale Wavelets and Coherence analysis and denoising by Continuous Wavelets Transform (다중 웨이브렛을 이용한 심전도(EEG) 신호 압축 및 연속 웨이브렛 변환을 이용한 Coherence분석 및 잡음 제거)

  • 이승훈;윤동한
    • 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.

Review of the Application of Wavelet Theory to Image Processing

  • Vyas, Aparna;Paik, Joonki
    • 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.

Three Dimensional Imaging Using Wavelets

  • Lee, Kyeong-Eun
    • 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.

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SPIHT Image Compression Using Biorthogonal Multiwavelets on [-1,1]

  • Yoo Sang-Wook;Kwon Seong-Geun;Kwon Ki-Ryong
    • 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.

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THE CHEREDNIK AND THE GAUSSIAN CHEREDNIK WINDOWED TRANSFORMS ON ℝd IN THE W-INVARIANT CASE

  • Hassini, Amina;Trimeche, Khalifa
    • 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.

A Concept of Fuzzy Wavelets based on Rank Operators and Alpha-Bands

  • Nobuhara, Hajime;Hirota, Kaoru
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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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.

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The Application of Wavelets to Measured Equation of Invariance

  • Lee, Byunfji;Youngki Cho;Lee, Jaemin
    • 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.

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An Efficient Adaptive Wavelet-Collocation Method Using Lifted Interpolating Wavelets (수정된 보간 웨이블렛응 이용한 적응 웨이블렛-콜로케이션 기법)

  • Kim, Yun-Yeong;Kim, Jae-Eun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.8
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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.

GEGENBAUER WAVELETS OPERATIONAL MATRIX METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS

  • UR REHMAN, MUJEEB;SAEED, UMER
    • 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.