• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.563-573
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• 2010

Using the fiberization technique of a shift-invariant space and the matrix characterization of the decomposition of a shift-invariant space of finite length into an orthogonal sum of singly generated shift-invariant spaces, we show that the main result in [13] can be interpreted as a statement about the length of a shift-invariant space, and give a more natural construction of multiwavelet frames from a frame multiresolution analysis of $L^2(\mathbb{R}^d)$.

• 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.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.40 no.1
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• pp.87-95
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• 2003

This paper proposes an object detection algorithm using the Multiresolution Motion Estimation(MRME) in wavelet d야main. A existing motion estimation method has characteristics of motion estimation but it requires having computation. Motion estimation in higher resolution used the motion vector of the lower resolution with the MRME that has parent-child relationship on wavelet coefficients. This method reduces the search area of motion estimation in higher resolution and computational complexity. The computational complexity of the proposed method is about 40% of the existing method using 3-level Set Partitioning in Hierarchical Trees(SPIHT) wavelet transform. The experimental results with the proposed method showed about 11% decrease of Mean Absolute Difference(MAD) and gains able to precise tracking of object.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.279-294
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• 2013

We are interested in an adaptive grid method for hyperbolic equations. A multiresolution analysis, based on a biorthogonal family of interpolating scaling functions and lifted interpolating wavelets, is used to dynamically adapt grid points according to the physical field profile in each time step. Traditional finite-difference schemes with fixed stencils produce high oscillations around sharp discontinuities. In this paper, we hybridize high-resolution schemes, which are suitable for capturing singularities, and apply a finite-difference approach to the scaling functions at non-singular points. We use a total variation diminishing Runge-Kutta method for the time integration. The computational cost is proportional to the number of points present after compression. We provide several numerical examples to verify our approach.

• 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.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1291-1296
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• 2003

The objective of the present research is to develop a wavelet-based multiscale adaptive Galerkin method for membrane eigenvalue analysis. Since approximate eigensolutions at a certain resolution level can be good guesses, which play an important role in typical iterative solvers, at the next resolution level, the multiresolution iterative solution approach by wavelets can improve the solutionconvergence rate substantially. The intrinsic difference checking nature of wavelets can be also utilized effectively to develop an adaptive strategy. The present wavelet-based approach will be implemented for the simplest vector iteration method, but some important aspects, such as convergence speedup, and the reduction in the number of nodes can be clearly demonstrated.

• The KIPS Transactions:PartB
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• v.8B no.3
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• pp.299-304
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• 2001

본 논문에서는 HDTR, 디지털 TV, 영상전화, 멀티미디어 영상 등의 다양한 영상에 적용할 수 있는 영상 부호화 기법을 제안한다. 효율적인 영상 압축을 위하여 움직임에 따른 인간의 시각 효과 특성을 결합한 영상 부호화 기법이다. 입력 영상은 웨이브릿 변환을 통하여 다해상도 영상으로 구성된다. 데이터 압축은 저주파수 대역의 움직임 벡터를 움직임 정도에 따라 고주파수 대역 성분들을 처리함에 의해 얻어진다. 즉, 공간과 방향 주파수에 감도에 따라 인간의 눈에 민감하지 않은 대역을 제거한다. 대역내의 모든 블록을 균일하게 처리하는 기존의 방법에 비해 제안한 방법은 같은 전송율에서 재생 영상의 우수한 화질을 얻었다.

• Journal of Broadcast Engineering
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• v.7 no.4
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• pp.368-375
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• 2002

In this paper, we apply multiresolution wavelet transform for the digital image watermarking. For better result, we insert watermark into the images and set a proper weighting factor for each subband based on HVS model. With proposed algorithm, we confirm that the image quality is satisfactory and this method outperforms the previous methods against image compression and cropping.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.7
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• pp.1515-1522
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• 1997

Several image coding algorithms have been developed for the telecommunication and multimedia systems with high image quality and high compression ratio. In order to achieve low entropy and distortion, the system should pay great cost of computation time and memory. In this paper, the uniform cubic lattice is chosen for Lattice Vector Quantization (LVQ) because of its generic simplicity. As a transform coding, the Discrete Wavelet Transform (DWT) is applied to the images because of its multiresolution property. The proposed algorithm is basically composed of the biorthogonal DWT and the uniform cubic LVQ. The multiresolution property of the DWT is actively used to optimize the entropy and the distortion on the basis of the distortion-rate function. The vector codebooks are also designed to be optimal at each subimage which is analyzed by the biorthogonal DWT. For compression efficiency, the vector codebook has different dimension depending on the variance of subimage. The simulation results show that the performance of the proposed coding mdthod is superior to the others in terms of the computation complexity and the PSNR in the range of entropy below 0.25 bpp.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.10B
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• pp.1813-1820
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• 2000

In this paper we proposed an efficient multiresolution motion estimation(MRME) algorithm using half-pixel accuracy motion estimation (HPAME) and characteristics of motion vectors in the baseband. Conventional MRME method needs exact motion vectors in the baseband because those are used as initial motion vectors in higher frequency subbands. Therefore the proposed method uses HPAME to estimate the motion vectors exactly in the baseband. Based on the characteristics of these motion vectors the motion vectors in the higher frequency subbands are selectively estimatied. That is motion vectors in the higher frequency subbands are estimated only for the blocks which have the half-pixel accuracy motion vectors in the baseband. In the proposed method by using HPAME in the baseband and selective motion estimation in the higher frequency subbands we can obtain reconstructed image with the similar quality with the conventional method though we reduce the computational complexity and the bit rate considerably.