• Kyungpook Mathematical Journal
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• 제55권1호
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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.

• 대한수학회논문집
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• 제15권2호
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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.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2002년도 추계 학술발표회 논문집
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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.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2001년도 춘계학술대회 학술발표 논문집
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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.

• 제어로봇시스템학회논문지
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• 제4권3호
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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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• 제18권6호
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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.

• 한국시뮬레이션학회논문지
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• 제10권3호
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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.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 1998년도 가을 학술발표논문집 Vol.25 No.2 (2)
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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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• 제61권2호
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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.

• 한국멀티미디어학회논문지
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• 제3권5호
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• pp.461-469
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• 2000

해석학 분야의 한 갈래인 웨이브릿 해석에서 CWT(continuous wavelet transform)는 Plancherel 형태의 복원정리가 성립하고, 웨이브릿 급수는 frame 이론과 다해상도 분석이론(multiresolution analysis; MRA)을 활용한 이산복원정리가 성립한다. 복원정리가 만들어짐에 따라 이에 상응하는 웨이브릿이 생성되는데, CWT에서는 허용조건(admissibility condition)을 만족하는 Basic 웨 이브릿이고, 웨이브릿 급수에서는 MRA를 이용한 Daubechies 웨이브릿, frame 이론을 이용한 Meyer 웨이브릿 등을 생각할 수 있다. 본 논문에서는 CWT에서 사용한 허용조건을 자연스럽게 확장함으로써 기존의 것보다 간편하고 활용도가 우수한 이 산복원정리를 발견하고, 이에 상응하는 보다 만들기 쉬운 새로운 형태의 $L^1$-웨이브릿 군을 개발함을 목적으로 한다. 본 연구에서 개발한 새로운 웨이브릿을 사용하여 시간-주파수에서의 신호 복원 및 분석에 응용한다.