• 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.

• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.175-190
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• 2010

One of the intractable problems in multiresolution structural analysis is the decoupling computation between scales, which can be realized by the operator-orthogonal wavelets based on the lifting scheme. The multiresolution finite element space is described and the formulation of multiresolution finite element models for structural problems is discussed. Various operator-orthogonal wavelets are constructed by the lifting scheme according to the operators of multiresolution finite element models. A dynamic multiresolution algorithm using operator-orthogonal wavelets is proposed to solve structural problems. Numerical examples demonstrate that the lifting scheme is a flexible and efficient tool to construct operator-orthogonal wavelets for multiresolution structural analysis with high convergence rate.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.3
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• pp.251-258
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• 2004

Since the multiscale wavelet-based numerical methods allow effective adaptive analysis, they have become new analysis tools. However, the main applications of these methods have been mainly on elliptic problems, they are rarely used for eigenvalue analysis. The objective of this paper is to develop a new multiscale wavelet-based adaptive Galerkin method for eigenvalue analysis. To this end, we employ the hat interpolation wavelets as the basis functions of the finite-dimensional trial function space and formulate a multiresolution analysis approach using the multiscale wavelet-Galerkin method. It is then shown that this multiresolution formulation makes iterative eigensolvers very efficient. The intrinsic difference-checking nature of wavelets is shown to play a critical role in the adaptive analysis. The effectiveness of the present approach will be examined in terms of the total numbers of required nodes and CPU times.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.305-334
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• 2005

The objective of this study is to analyze the decay characteristics of the hat interpolation wavelet coefficients of some smooth functions defined in a two-dimensional space. The motivation of this research is to establish some fundamental mathematical foundations needed in justifying the adaptive multiresolution analysis of the hat-interpolation wavelet-Galerkin method. Though the hat-interpolation wavelet-Galerkin method has been successful in some classes of problems, no complete error analysis has been given yet. As an effort towards this direction, we give estimates on the decaying ratios of the wavelet coefficients at children interpolation points to the wavelet coefficient at the parent interpolation point. We also give an estimate for the difference between non-adaptively and adaptively interpolated representations.

• KIEE International Transactions on Power Engineering
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• v.3A no.3
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• pp.130-138
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• 2003

This paper presents a discrete wavelet transform approach for determining the beginning and end times of voltage sags. Firstly, investigations in the use of some typical mother wavelets, namely Daubechies, Symlets, Coiflets and Biorthogonal are carried out and the most appropriate mother wavelet is selected. The proposed technique is based on utilizing the maximum value of Dl (at scale 1) coefficients in multiresolution analysis (MRA) based on the discrete wavelet transform. The results are compared with other methods for determining voltage sag duration, such as the Root Mean Square (RMS) voltage and Short Time Fourier Transform (STFT) methods. It is shown that the voltage sag detection technique based on the wavelet transform is a satisfactory and reliable method for detecting voltage sags in power quality disturbance analysis.

• Journal of the Korean Association of Geographic Information Studies
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• v.4 no.3
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• pp.61-70
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• 2001

This paper presents a new method to extract semi-automatically roads from high spatial resolution satellite imagery. This method is based both on wavelet transform and on multiresolution analysis combined in the "$\grave{a}$ trous" algorithm. As an urban road network consists on different classes of streets, multiresolution processing allows to extract the streets class by class. The method was applied to a KVR-1000 image on a part of Busan Metropolitan City. The method was carried out for the road extraction of three different widths and it succeeded in extracting good fitted strips. The accuracy analysis for three types of streets was also performed. The overall accuracy in 4 pixels of width is 80.5%. The result suggests that this method can be used to update road networks in the studied urban network. In summary, the multiresolution approach based on the wavelet transform, used in this study, is regarded as one of effective methods to extract urban road network from high spatial resolution satellite images.

• KIEE International Transactions on Power Engineering
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• v.11A no.4
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• pp.1-8
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• 2001

This paper presents a discrete wavelet transform approach for detecting voltage sags initialized by fault conditions and starting of larger motors. The proposed technique is based on utilizing the summation value of D1(at scale 1) coefficients in multiresolution analysis(MRA) based on the discrete wavelet transform. In this paper, the proposed technique is tested under various cases of voltage sags. It is shown that the voltage sag detection technique based on the wavelet transform is a satisfactory and reliable method for detecting voltage sags in power quality disturbance analysis.

• Structural Engineering and Mechanics
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• v.33 no.2
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• pp.179-191
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• 2009

This paper is aimed at combining wavelet multiresolution analysis and nonstationary Kanai-Tajimi model for the simulation of earthquake accelerograms. The proposed approach decomposes earthquake accelerograms using wavelet multiresolution analysis for the simulation of earthquake accelerograms. This study is on the basis of some Iranian earthquake records, namely Naghan 1977, Tabas 1978, Manjil 1990 and Bam 2003. The obtained results indicate that the simulated records preserve the significant properties of the actual accelerograms. In order to investigate the efficiency of the model, the spectral response curves obtained from the simulated accelerograms have been compared with those from the actual records. The results revealed that there is a good agreement between the response spectra of simulated and actual records.

• Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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• 2000.11a
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• pp.183-187
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• 2000

This paper deals with multiresolution analysis of wavelet transform for partial discharge(PD), both corona and surface discharge. Multiresolution analysis was used for performing discrete wavelet transform. PD signals was decomposed into "approximation" and "detail" components until 4 levels by using discrete wavelet analysis. In this paper, daubechies family is adopted for the research of the characteristics of PD signals. The results show that in corona discharge the segment 7, 8, 9, 10, 11 values of defined variable is increased with discharge process, so phase distribution is characterized by 210~330 ranges. In case surface discharge in expoxy insulator inserted, defined variable values is fairly symmetric discharge pattern because coupled both corona and dielectric bounded discharges. We can confirmly discriminate the type PD source. the type PD source.

• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.153-166
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• 2008

This paper suggests the use of wavelet multiresolution analysis (WMRA) and neural network for generation of artificial earthquake accelerograms from target spectrum. This procedure uses the learning capabilities of radial basis function (RBF) neural network to expand the knowledge of the inverse mapping from response spectrum to earthquake accelerogram. In the first step, WMRA is used to decompose earthquake accelerograms to several levels that each level covers a special range of frequencies, and then for every level a RBF neural network is trained to learn to relate the response spectrum to wavelet coefficients. Finally the generated accelerogram using inverse discrete wavelet transform is obtained. An example is presented to demonstrate the effectiveness of the method.