• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.127-135
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• 2015

We determine two-interval normalized tight frame wavelet sets for real dilation $d{\in}(1,{\infty})$, and characterize all symmetric normalized tight frame wavelet sets. We also construct a normalized tight frame wavelet set which has an infinite number of components accumulating at the origin. These normalized tight frame wavelet sets and their closures possess the same measure. Finally an example of a normalized tight frame wavelet set is provided whose measure is strictly less than the measure of its closure.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.285-308
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• 2000

We generalize bi-orthogonal (non-orthogona) MRA to frame MRA in which the family of integer translates of a scaling func-tion forms a frame for the initial ladder space V0. We investigate the internal structure of frame MRA and establish the existence of a dual scaling function, and show that, unlike bi-orthogonal MRA, there ex-ists a frame MRA that has no (frame) 'wavelet'. Then we prove the existence of a dual wavelet under the assumption of the existence of a wavelet and present easy sufficient conditions for the existence of a wavelet. Finally we give a new proof of an equivalent condition for the translates of a function in L2(R) to be a frame of its closed linear span.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2002.09a
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• pp.173-180
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• 2002

This paper presents a signal processing procedure to detect damage locations of frame structures by using continuous wavelet transform. Morlet wavelet is used as a mother wavelet in wavelet transform. Wavelet transform has the characteristics that allows the use of long time intervals at more precise low-frequency information, and shorter regions at high-frequency information. By this wavelet transform characteristics, Morlet wavelet may be used to identify the locations of damages in the structures. The numerical case studies show that this method can be applied to detect the damage location under a controlled sweeping load.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.57-60
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• 2001

In this paper, we propose growing algorithm of wavelet neural network. It is growing algorithm that adds hidden nodes using wavelet frame which approximately supports orthogonality in wavelet neural network based on wavelet theory. The result of this processing can be reduced global error and progresses performance efficiency of wavelet neural network. We apply the proposed algorithm to approximation problem and evaluate effectiveness of proposed algorithm.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.3
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• pp.372-377
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• 1998

This paper deals with the detection, feature extraction and classification of surface defects in cold rolled strips. Inspection systems are one of the most important fields in factory automation. Defects such as slipmark and dullmark can be effectively detected with a Gaussian matched filter because their shapes are similar to Gaussian. It is justified that the proposed WF(Wavelet Frame) method could be regarded as multiscale Gaussian matched filter which can be applied to the inspection of cold rolled strip. After a wavelet frame transform, the entropies and moments are computed for each subband which pass through both local low pass filter and nonlinear operator. With these features as input, a MLP(Multi Layer Perceptron) is used as a classifier. The proposed inspection method was applied to the real images with defects, and hence showed good performance. The role of each extracted feature is analyzed by KLT(Karhunen-Loeve Transform).

• Smart Structures and Systems
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• v.18 no.6
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• pp.1189-1202
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• 2016

This paper describes an application of wavelet analysis for damage detection of a steel frame structure with bolted connections. The wavelet coefficients of the acceleration response for the healthy and loosened connection structure were calculated at each measurement point. The difference of the wavelet coefficients of the response of the healthy and loosened connection structure is selected as an indicator of the damage. At each node of structure the norm of the difference of the wavelet coefficients matrix is then calculated. The point for which the norm has the higher value is a candidate for location of the damage. The above procedure was experimentally verified on a laboratory-scale 2-meter-long steel frame. The structure consists of 11 steel beams forming a four-bay frame, which is subjected to impact loads using a modal hammer. The accelerations are measured at 20 different locations on the frame, including joints and beam elements. Two states of the structure are considered: healthy and damaged one. The damage is introduced by means of loosening two out of three bolts at one of the frame connections. Calculating the norm of the difference of the wavelet coefficients matrix at each node the higher value was found to be at the same location where the bolts were loosened. The presented experiment showed the effectiveness of the wavelet approach to damage detection of frame structures assembled using bolted connections.

• Journal of the Korea Society for Simulation
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• v.10 no.3
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• pp.95-103
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• 2001

Rendering of 3D terrain data in real-time is difficult because of its large scale. So, it is necessary to use level-of-detail(LOD) that uses fewer data, but makes almost similar image to the original. We present an algorithm for real-time LOD generation and rendering of 3D terrain data. The algorithm applies wavelet transform to the terrain data, and then generates quadtree based view-dependent LOD using wavelet coefficients that are the output of wavelet transform. It also uses frame-to-frame coherence and view culling for high frame rates.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10c
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• pp.509-511
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• 1998

본 논문에서는 동영상 데이터베이스에서 Key-frame을 검색하는 방법을 제안한다. 본 논문에서는 Key-frame을 검색하기위해 컬러 피쳐를 공간영역에서 추출하지 않고 wavelet transform 영역에서 컬러 피쳐를 추출하는 방법을 제안한다. wavelet transform 의 저주파 밴드는 영상전체의 특징을 잘 나타내고 고주파 밴드는 texture 와 국부적인 컬러 특성을 잘 나타낸다. 색인과정 알고리즘은 영상의 크기를 정규화하고 RGB 컬러공간에서 HSV 컬러 공간으로 변환을 하여, H, S, V 각 채널에 대해 Daubechies' wavelet transform을 수행한 후 변환 영역에서 피쳐를 추출하게 된다. 색인을 위한 피쳐로 wavelet 계수와 lowest 밴드의 평균과 표준편차를 추출하였다. 효율적인 검색을 위해 검색은 2단계로 수행된다. 먼저 평균과 표준편차만을 이용한 1차 검색을 통해 2차 검색의 후보 영상들을 추출하고 2차 검색에서는 1차 검색 통과 영상들에 대해서만 wavelet 계수들을 비교하여 최종 검색 결과를 얻게 된다. 검색결과 기존의 컬러 피쳐를 이용한 방법보다 우수한 검색결과를 얻을 수 있었다.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.371-381
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• 2021

In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet frame sets in locally compact abelian groups. The condition is generated by modulating a collection of characteristic functions that correspond to a generalized shift-invariant system via the Fourier transform. We present two approaches (for stationary and non-stationary wavelets) to construct the scaling function for L²(G) and, using the scaling function, we construct an orthonormal wavelet basis for L²(G). We propose an open problem related to the extension principle for Riesz wavelets in locally compact abelian groups.

• Journal of Korea Multimedia Society
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• v.3 no.5
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• pp.461-469
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• 2000

A wavelet analysis in a field of analytics is to create a reconstruction theorem of Plancherel form. And a series of wavelet is to create a discrete is to create a discrete reconstruction theorem for a frame theory and a multiresolution analysis theory. As a generation of reconstruction theorem, a wavelet correspond to it is generated. That is to be like a basic wavelet which is satisfied an admissibility condition in CWT and a Daubechies wavelet using MRA in wavelet series and a Meyer wavelet using a frame theory. In this paper, we discover a discrete reconstruction theorem which is superior to a conventional discrete reconstruction theorem by extending admissibility condition used in CWT and develop a New $L^1$-wavelet group. A new $L^1$-wavelet is applied to a signal reconstruction and a signal analysis in time-frequency region.