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wavelet transform for Fresnel-transformed mother wavelets

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Chinese Physics B 2011年第12期20卷 57-62页

作者：刘述光陈俊华范洪义 School of Mathematics and Physics Anhui Polytechnic University Department of Materials Science and Engineering University of Science and Technology of China

In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state itself vary from ｜ψ〉 to Ftr, s ｜ψ〉, except for variation within the family of dilations and translations. The Parseval＇s equality, admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed. By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform, we obtain some mother wavelets. A comparison between the newly found mother wavelets is presented.

关键词： wavelet transform fresnel transformation quantum state vector

wavelet transform of Velocity-Time Data for the Analysis of Turbulent Structures in a Trayed Bubble Column

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Chinese Journal of Chemical Engineering 2004年第5期12卷 622-627页

作者：闻建平贾晓强周怀刘宝谈李瑞 Department of Biochemical Engineering School of Chemical Engineering and Technology Tianjin University Tianjin 300072 China Distillation Laboratory of State Key Laboratories of Chemical Engineering Tianjin University Tianjin 300072 China

Hydrodynamic and turbulent structures in the trayed bubble column with 1.2 m inner diameter have been characterized from liquid-phase velocity-time series data obtained by the hot-film anemometer. wavelet transform analysis was used for denoising the measured data and also for evaluating quantifiers of turbulence, viz., local intermittency measure, intermittency index and flatness factor. These quantifiers help in detecting the passage of bubbles and reveal the hidden structures and patterns in data. Also, the wavelet scalewise analysis of the turbulence at various locations in the column and under different operating conditions could be used to build a direct relationship between the local gas holdup and flatness factor. The methodology is therefore suitable for online evaluation of the trayed bubble column performance and shows promise for developing strategies for improving process performance.

关键词： wavelet transform trayed bubble column hydrodynamics turbulencestructures hot film anemometer

THE wavelet transform OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION

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Applied Mathematics and Mechanics(English Edition) 2002年第9期23卷 1062-1070页

作者：刘海峰周炜星王辅臣龚欣于遵宏 College of Resource and Environmental Engineering East China University of Science and TechnologyShanghai 200237P R China

Some properties of the wavelet transform of trigonometric Junction, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with this equation agrees well with the function.

关键词： wavelet transform periodic function nonstationary periodic function Fourier transform

wavelet transform and Radon transform on the Quaternion Heisenberg Group

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Acta Mathematica Sinica,English Series 2014年第4期30卷 619-636页

作者： Jian Xun HE He Ping LIU School of Mathematics and Information Sciences Guangzhou University Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes Guangzhou University LMAM School of Mathematical SciencesPeking University

Let be the quaternion Heisenberg group, and let P be the affine automorphism group of . We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on L2（）. A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the Radon transform on . . A Semyanistyi-Lizorkin space is introduced, on which the Radon transform is a bijection. We deal with the Radon transform on both by the Euclidean Fourier transform and the group Fourier transform. These two treatments are essentially equivalent. We also give an inversion formula by using wavelets, which does not require the smoothness of functions if the wavelet is smooth. In addition, we obtain an inversion formula of the Radon transform associated with the sub-Laplacian on .

关键词： Quaternion Heisenberg group wavelet transform Radon transform inverse Radon transform

wavelet transform-Based High-Definition Map Construction From a Panoramic Camera

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Journal of Shanghai Jiaotong university(Science) 2021年第5期26卷 569-576页

作者： ZHUANG Hanyang ZHOU Xuejun WANG Chunxiang QIAN Yuhan University of Michigan-Shanghai Jiao Tong University Joint Institute Shanghai Jiao Tong UniversityShanghai 200240China Guangxi Key Laboratory of Automobile Components and Vehicle Technology Guangxi University of Science and TechnologyLiuzhou 545006GuangxiChina Noblelift Intelligent Equipment Co. Ltd.Huzhou 313100ZhejiangChina Department of Automation Shanghai Jiao Tong UniversityShanghai 200240China Key Laboratory of System Control and Information Processing of Ministry of Education Shanghai 200240China School of Mechanical Engineering Shanghai Jiao Tong UniversityShanghai 200240China

High-definition(HD)maps are key components that provide rich topologic and semantic information for decision-making in vehicle autonomous driving systems.A complete ground orthophoto is usually used as the base image to construct the HD *** ground orthophoto is obtained through inverse perspective transformation and image *** the image mosaicing,multiple consecutive orthophotos are stitched together using pose information and image *** this study,wavelet transform is introduced to the image mosaicing process to alleviate the information loss caused by image *** the orthophoto wavelet transform,high-frequency and low-frequency components are fused using different strategies to form a complete base image with clearer local *** results show that the accuracy of the orthophotos generated using this method is improved.

关键词： high-definition(HD)map wavelet transform image registration panorama

wavelet transform Approach to Segment Thermal Image

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Journal of Beijing Institute of Technology 2003年第S1期12卷 33-38页

作者：付梦印张长江李杰金梅 Department of Automatic Control School of Information and Science TechnologyBeijing Institute of Technology Beijing 100081China School of Electrics and Information Engineering Daqing Petroleum InstituteDaqingHeilongiang 163318.China

An efficient multi-threshold approach to segment thermal image is given based on wavelet transform. The gray-level histogram of original image is obtained. In order to reduce the effect of noise, the gray-level histogram is smoothed by Bezier curve and Bezier histogram is obtained. One dimension stationary wavelet transform is done to the curvature curve of Bezier histogram. Positions of peak values of curvature curve in wavelet domain are adjusted from 'fine-to-coarse' at all scales. The gray level values, which are located in adjusted peak values at all scales, are considered as segmentation thresholds. The gray level values of valley between peaks are considered as quantity gray levels. Optimal segmentation scale is obtained by a cost criterion. The results of experiment show that a target can be segmented effectively from complex background in thermal image by new approach.

关键词： wavelet transform thermal image segmentation Bezier histogram curvature

wavelet transform and gradient direction based feature extraction method for off-line handwritten Tibetan letter recognition

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Journal of Southeast University(English Edition) 2014年第1期30卷 27-31页

作者：黄鹤鸣达飞鹏韩晓旭东南大学自动化学院南京210096 青海师范大学计算机学院西宁810008 福坦莫大学计算机与信息科学系纽约10458

To improve the recognition accuracy of off-line handwritten Tibetan characters the local gradient direction histograms based on the wavelet transform are proposed as the recognition *** for a Tibetan character sample image the first level approximation component of the Haar wavelet transform is *** the approximation component is partitioned into several equal-sized zones. Finally the gradient direction histograms of each zone are calculated and the local direction histograms of the approximation component are considered as the features of the character sample *** proposed method is tested on the recently developed off-line Tibetan handwritten character sample *** experimental results demonstrate the effectiveness and efficiency of the proposed feature extraction *** compared with the detail components the approximation component contributes more to the recognition accuracy.

关键词： pattern recognition wavelet transform gradient direction Tibetan handwritten character

New reclosing scheme of distribution system for utilization of BESS using wavelet transform

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Journal of Central South University 2018年第1期25卷 78-83页

作者： PARK Keon-Woo KIM Chul-Hwan LEE Sang-Hyuk RHEE Sang-Bong College of Info.& Comm. Eng Sungkyunkwan UniversitySuwon16419Korea Department of Electrical and Electronic Engineering of Xi’an Jiaotong-Liverpool University (XJTLU) Suzhou 215123 China Department of Electrical Engineering Yeungnam University Gyeongsan 38541 Korea

This paper proposed the reclosing method in distribution system with battery energy storage system(BESS)using wavelet transform(WT).The proposed method performs the WT of load current and then calculates the absolute value of slope of detail *** mother wavelet used is db4of *** fault clearing is detected using the rapid increase of this *** the detection of fault clearing,the reclosing is *** verify the proposed method,various simulations according to the fault clearing times,fault resistances,and fault lengths are performed using *** simulation results show that fault clearing can be detected using proposed absolute value of slope of detail coefficient and hence the reclosing can be performed successfully.

关键词： distribution system electro-magnetic transient program reclosing battery energy storage system wavelet transform

Transient-Spatial Pattern Mining of Eddy Current Pulsed Thermography Using wavelet transform

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Chinese Journal of Mechanical Engineering 2014年第4期27卷 768-778页

作者： YANG Hailong GAO Bin TIAN Guiyun REN Wenwei WOO Wai Lok School of Automation Engineering University of Electronic Science and Technology of China School of Electrical and Electronic Engineering Newcastle University

Eddy current pulsed thermography（ECPT） is an emerging Non-destructive testing and evaluation（NDT E） technique, which uses hybrid eddy current and thermography NDT E techniques that enhances the detectability from their compensation. Currently, this technique is limited by the manual selection of proper contrast frames and the issue of improving the efficiency of defect detection of complex structure samples remains a challenge. In order to select a specific frame from transient thermal image sequences to maximize the contrast of thermal variation and defect pattern from complex structure samples, an energy driven approach to compute the coefficient energy of wavelet transform is proposed which has the potential of automatically selecting both optimal transient frame and spatial scale for defect detection using ECPT. According to analysis of the variation of different frequency component and the comparison study of the detection performance of different scale and wavelets, the frame at the end of heating phase is automatically selected as an optimal transient frame for defect detection. In addition, the detection capabilities of the complex structure samples can be enhanced through proper spatial scale and wavelet selection. The proposed method has successfully been applied to low speed impact damage detection of carbon fibre reinforced polymer（CFRP） composite as well as providing the guidance to improve the detectability of ECPT technique.

关键词： non-destructive testing and evaluation composite impact damage detection wavelet transform energy driven approach transient-spatial analysis