• 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.

• 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 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.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8 s.179
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• pp.2091-2099
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• 2000

The object of the present study is to present an adaptive wavelet-Galerkin method for the analysis of thin-walled box beam. Due to good localization properties of wavelets, wavelet methods emerge as alternative efficient solution methods to finite element methods. Most structural applications of wavelets thus far are limited in fixed-scale, non-adaptive frameworks, but this is not an appropriate use of wavelets. On the other hand, the present work appears the first attempt of an adaptive wavelet-based Galerkin method in structural problems. To handle boundary conditions, a fictitous domain method with penalty terms is employed. The limitation of the fictitious domain method is also addressed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.12
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• pp.1608-1615
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• 2004

CFD data compression methods based on Full-3D and Quasi-1D supercompact multiwavelets are presented. Supercompact wavelets method provide advantageous benefit that it allows higher order accurate representation with compact support. Therefore it avoids unnecessary interaction with remotely located data across singularities such as shock. Full-3D wavelets entails appropriate cross-derivative scaling function & wavelets, hence it can allow highly accurate multi-spatial data representation. Quasi-1D method adopt 1D multiresolution by alternating the directions rather than solving huge transformation matrix in Full-3D method. Hence efficient and relatively handy data processing can be conducted. Several numerical tests show swift data processing as well as high data compression ratio for CFD simulation data.

• The Journal of the Korea institute of electronic communication sciences
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• v.19 no.1
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• pp.113-118
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• 2024

In this paper, we propose an optimal wavelet in a system for canceling background noise of acoustic signals. This system performed Discrete Wavelet Transform(DWT) instead of the existing Short Time Fourier Transform(STFT) and then improved noise cancellation performance through a deep learning process. DWT functions as a multi-resolution band-pass filter and obtains transformation parameters by time-shifting the parent wavelet at each level and using several wavelets whose sizes are scaled. Here, the noise cancellation performance of several wavelets was tested to select the most suitable mother wavelet for analyzing the speech. In this study, to verify the performance of the noise cancellation system for various wavelets, a simulation program using Tensorflow and Keras libraries was created and simulation experiments were performed for the four most commonly used wavelets. As a result of the experiment, the case of using Haar or Daubechies wavelets showed the best noise cancellation performance, and the mean square error(MSE) was significantly improved compared to the case of using other wavelets.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.6
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• pp.69-74
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• 2023

In this paper we review techniques for building and analyzing wavelets on irregular point sets in one and two dimensions. In particular we focus on subdivision schemes and commutation. Subdivision means the skill that approximates the initial lines or mesh into a tender curve or a curved surface by continuous partitioning operation. The key to generalizing wavelet constructions to non-traditional settings is the use of generalized subdivision. The first generation setting is already connected with subdivision schemes, but they become even more important in the construction of second generation wavelets. Subdivision schemes provide fast algorithms, create a natural multi-resolution structure, and yield the underlying scaling functions and wavelets we seek.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.4 s.304
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• pp.39-48
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• 2005

This paper proposes novel texture segmentation method using Bayesian estimation method and neural networks. We use multi-scale wavelet coefficients and the context information of neighboring wavelets coefficients as the input of networks. The output of neural networks is modeled as a posterior probability. The context information is obtained by HMT(Hidden Markov Tree) model. This proposed segmentation method shows better performance than ML(Maximum Likelihood) segmentation using HMT model. And post-processed texture segmentation results as using multi-scale Bayesian image segmentation technique called HMTseg in each segmentation by HMT and the proposed method also show that the proposed method is superior to the method using HMT.

• Journal of Mechanical Science and Technology
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• v.20 no.1
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• pp.110-124
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• 2006

The multi scale wavelet-Galerkin method implemented in an adaptive manner has an advantage of obtaining accurate solutions with a substantially reduced number of interpolation points. The method is becoming popular, but its numerical efficiency still needs improvement. The objectives of this investigation are to present a new numerical scheme to improve the performance of the multi scale adaptive wavelet-Galerkin method and to give detailed implementation procedure. Specifically, the subdomain technique suitable for multiscale methods is developed and implemented. When the standard wavelet-Galerkin method is implemented without domain subdivision, the interaction between very long scale wavelets and very short scale wavelets leads to a poorly-sparse system matrix, which considerably worsens numerical efficiency for large-sized problems. The performance of the developed strategy is checked in terms of numerical costs such as the CPU time and memory size. Since the detailed implementation procedure including preprocessing and stiffness matrix construction is given, researchers having experiences in standard finite element implementation may be able to extend the multi scale method further or utilize some features of the multiscale method in their own applications.