• IEIE Transactions on Smart Processing and Computing
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• 제5권6호
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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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• 제35권2호
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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.

• 대한기계학회논문집A
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• 제28권3호
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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.

• 대한수학회지
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• 제42권2호
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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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• 제3A권3호
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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.

• 한국지리정보학회지
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• 제4권3호
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• pp.61-70
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• 2001

본 연구에서는 고해상도 영상을 도시 도로망 자료 갱신에 이용하기 위한 새로운 반자동적 방법을 소개하고 이를 부산광역시 일부 지역의 KVR-1000 영상에 적용하여 그 결과를 평가하였다. 이 기법은 웨이블릿 변환을 이용하여 다중해상도 분석을 수행하는 것으로, 도시의 다양한 유형의 도로망을 추출 가능하게 해준다. 본 연구에서는 "$\grave{a}$ trous" 알고리즘을 이용하여 다중해상도 분석 작업을 수행하였으며, 도로는 대로, 중로, 소로로 구분하여 추출하였다. 추출 결과는 매우 양호하여 8 m 해상도의 경우 전체 정확도는 80.5%이었다. 또한 도로의 형태별로도 정확도를 평가하였는데, 직선도로의 정확도가 곡선도로 및 교차로에 비해 우수하였다. 따라서 곡선도로 추출의 정확도를 높이는 기법이 보완된다면, 본 연구는 우리나라의 도시 도로망 데이터베이스 구축에 유용하게 활용될 수 있을 것이다.

• KIEE International Transactions on Power Engineering
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• 제11A권4호
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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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• 제33권2호
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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.

• 한국조명전기설비학회:학술대회논문집
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• 한국조명전기설비학회 2000년도 학술대회논문집
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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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• 제28권2호
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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.