Plant diseases are a major threat that can severely impact the production of agriculture and forestry.This can lead to the disruption of ecosystem functions and health.With its ability to capture continuous narrow-ban...Plant diseases are a major threat that can severely impact the production of agriculture and forestry.This can lead to the disruption of ecosystem functions and health.With its ability to capture continuous narrow-band spectra,hyperspectral technology has become a crucial tool to monitor crop diseases using remote sensing.However,existing continuous wavelet analysis(CWA)methods suffer from feature redundancy issues,while the continuous wavelet projection algorithm(CWPA),an optimization approach for feature selection,has not been fully validated to monitor plant diseases.This study utilized rice bacterial leaf blight(BLB)as an example by evaluating the performance of four wavelet basis functions-Gaussian2,Mexican hat,Meyer,andMorlet-within theCWAandCWPAframeworks.Additionally,the classification models were constructed using the k-nearest neighbors(KNN),randomforest(RF),and Naïve Bayes(NB)algorithms.The results showed the following:(1)Compared to traditional CWA,CWPA significantly reduced the number of required features.Under the CWPA framework,almost all the model combinations achieved maximum classification accuracy with only one feature.In contrast,the CWA framework required three to seven features.(2)Thechoice of wavelet basis functions markedly affected the performance of themodel.Of the four functions tested,the Meyer wavelet demonstrated the best overall performance in both the CWPA and CWA frameworks.(3)Under theCWPAframework,theMeyer-KNNandMeyer-NBcombinations achieved the highest overall accuracy of 93.75%using just one feature.In contrast,under the CWA framework,the CWA-RF combination achieved comparable accuracy(93.75%)but required six features.This study verified the technical advantages of CWPA for monitoring crop diseases,identified an optimal wavelet basis function selection scheme,and provided reliable technical support to precisely monitor BLB in rice(Oryza sativa).Moreover,the proposed methodological framework offers a scalable approach for the early diagnosis and assessment of plant stress,which can contribute to improved accuracy and timeliness when plant stress is monitored.展开更多
Cardiovascular diseases are the world’s leading cause of death;therefore cardiac health of the human heart has been a fascinating topic for decades.The electrocardiogram(ECG)signal is a comprehensive non-invasive met...Cardiovascular diseases are the world’s leading cause of death;therefore cardiac health of the human heart has been a fascinating topic for decades.The electrocardiogram(ECG)signal is a comprehensive non-invasive method for determining cardiac health.Various health practitioners use the ECG signal to ascertain critical information about the human heart.In this article,swarm intelligence approaches are used in the biomedical signal processing sector to enhance adaptive hybrid filters and empirical wavelet transforms(EWTs).At first,the white Gaussian noise is added to the input ECG signal and then applied to the EWT.The ECG signals are denoised by the proposed adaptive hybrid filter.The honey badge optimization(HBO)algorithm is utilized to optimize the EWT window function and adaptive hybrid filter weight parameters.The proposed approach is simulated by MATLAB 2018a using the MIT-BIH dataset with white Gaussian,electromyogram and electrode motion artifact noises.A comparison of the HBO approach with recursive least square-based adaptive filter,multichannel least means square,and discrete wavelet transform methods has been done in order to show the efficiency of the proposed adaptive hybrid filter.The experimental results show that the HBO approach supported by EWT and adaptive hybrid filter can be employed efficiently for cardiovascular signal denoising.展开更多
Phase spectrum estimation of the seismic wavelet is an important issue in high-resolution seismic data processing and interpretation. On the basis of two patterns of constant-phase rotation and root transform for wave...Phase spectrum estimation of the seismic wavelet is an important issue in high-resolution seismic data processing and interpretation. On the basis of two patterns of constant-phase rotation and root transform for wavelet phase spectrum variation, we introduce six sparse criteria, including Lu’s improved kurtosis criterion, the parsimony criterion, exponential transform criterion, Sech criterion, Cauchy criterion, and the modified Cauchy criterion, to phase spectrum estimation of the seismic wavelet, obtaining an equivalent effect to the kurtosis criterion. Through numerical experiments, we find that when the reflectivity is not a sparse sequence, the estimated phase spectrum of the seismic wavelet based on the criterion function will deviate from the true value. In order to eliminate the influence of non-sparse reflectivity series in a single trace, we apply the method to the multi-trace seismogram, improving the accuracy of seismic wavelet phase spectrum estimation.展开更多
The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wave...The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal＇ s instantaneous amplitude and period.展开更多
A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. Wit...A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. With good features in treating singularities, Haar series solution converges rapidly for arbitrary distributions, especially for the case where the material properties change rapidly in some regions. Through numerical examples the influences of the ratio of material constants on the top and bottom surfaces and different material gradient distributions on the structural response of the plate to mechanical stimuli are studied.展开更多
The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matri...The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.展开更多
In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a nove...In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a novel steganographic method based on wavelet and modulus function is presented. First, an image is divided into blocks of prescribed size, and every block is decomposed into one-level wavelet. Then, the capacity of the hidden secret data is decided with the number of wavelet coefficients of larger magnitude. Finally, secret information is embedded by steganography based on modulus function. From the experimental results, the proposed method hides much more information and maintains a good visual quality of stego-image. Besides, the embedded data can be extracted from the stego-image without referencing the original image.展开更多
In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which th...In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression.展开更多
Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructio...Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructions of orthogonal wavelet filters are put forward, respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.展开更多
The relations between Gaussian function and Γ function is revealed first at one dimensional situation. Then, the Fourier transformation of n dimensional Gaussian function is deduced by a lemma. Following th...The relations between Gaussian function and Γ function is revealed first at one dimensional situation. Then, the Fourier transformation of n dimensional Gaussian function is deduced by a lemma. Following the train of thought in one dimensional situation, the relation between n dimensional Gaussian function and Γ function is given. By these, the possibility of arbitrary derivative of an n dimensional Gaussian function being a mother wavelet is indicated. The result will take some enlightening role in exploring the internal relations between Gaussian function and Γ function as well as in finding high dimensional mother wavelets.展开更多
Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is ort...Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.展开更多
Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined by finite sets of...Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined by finite sets of parameters. Application to compression of fractal functions are also discussed.展开更多
Over the past decade, wavelets provided a powerful and flexible set of tools for handling fundamental problems in science and engineering. Wavelet analyses are being used for solving problems in different engineering ...Over the past decade, wavelets provided a powerful and flexible set of tools for handling fundamental problems in science and engineering. Wavelet analyses are being used for solving problems in different engineering areas like audio de-noising, signal compression, object detection, image decomposition, speech recognition etc. Wavelet analysis employs orthonormal as well as non-orthonornal functions. This research investigates the effectiveness of wavelet analysis in detecting defects in underground steel pipe networks. Continuous Wavelet Transforms （CWT） has been performed on the received signals of cylindrical guided waves. Cylindrical Guided waves are generated and propagated through the pipe wall boundaries in a pitch-catch system. Piezo-electric transducers are used to generate as well as receive guided waves. Several mother wavelet functions such as Daubechies, Symlet, Coiflet and Meyer have been used for the Continuous Wavelet Transform to investigate the most suitable function for defect detection. This research also investigates the effect of surrounding soil on wavelet transforms for different mother wavelet functions.展开更多
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 spect...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.展开更多
We derive the conditions for the existence of the unique solution of the two scale integral equation and the form of the solution, according to the method of the construction of the dyadic scale function. We give the ...We derive the conditions for the existence of the unique solution of the two scale integral equation and the form of the solution, according to the method of the construction of the dyadic scale function. We give the construction of the dyadic wavelet and its necessary and sufficient condition. As an application, we also develop a pyramid algorithm of the dyadic wavelet decomposition.展开更多
A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initi...A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initial model be-ing taken, a generalized least-squares inversion procedure is gradually carried out for receiver function from low to high scale, with the inversion result for low order receiver function as the initial model for high order. A neighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradu-ally focus at the global minimum by introducing high scale information of receiver function. With the gradual ad-dition of high wave-number to smooth background velocity structure, wavelet transformation can keep the inver-sion result converge to the global minimum, reduce to certain extent the dependence of inversion result on the initial model, overcome the nonuniqueness of generalized least-squares inversion, and obtain reliable crustal and upper mantle velocity with high resolution.展开更多
Temporal activity patterns in animals emerge from complex interactions between choices made by organisms as responses to biotic interactions and challenges posed by external factors. Temporal activity pattern is an in...Temporal activity patterns in animals emerge from complex interactions between choices made by organisms as responses to biotic interactions and challenges posed by external factors. Temporal activity pattern is an inherently continuous process, even being recorded as a time series. The discreteness of the data set is clearly due to data-acquisition limitations rather than a true underlying discrete nature of the phenomenon itself. Therefore, curves are a natural representation for high-frequency data. Here, we fully model temporal activity data as curves integrating wavelets and functional data analysis, allowing for testing hypotheses based on curves rather than on scalar and vector-valued data. Temporal activity data were obtained experimentally for males and females of a small-bodied marsupial and modelled as wavelets with independent and identically distributed errors and dependent errors. The null hypothesis of no difference in temporal activity pattern between male and female curves was tested with functional analysis of variance (FANOVA). The null hypothesis was rejected by FANOVA and we discussed the differences in temporal activity pattern curves between males and females in terms of ecological and life-history attributes of the reference species. We also performed numerical analysis that shed light on the regularity properties of the wavelet bases used and the thresholding parameters.展开更多
An efficient face recognition system with face image representation using averaged wavelet packet coefficients, compact and meaningful feature vectors dimensional reduction and recognition using radial basis function ...An efficient face recognition system with face image representation using averaged wavelet packet coefficients, compact and meaningful feature vectors dimensional reduction and recognition using radial basis function (RBF) neural network is presented. The face images are decomposed by 2-level two-dimensional (2-D) wavelet packet transformation. The wavelet packet coefficients obtained from the wavelet packet transformation are averaged using two different proposed methods. In the first method, wavelet packet coefficients of individual samples of a class are averaged then decomposed. The wavelet packet coefficients of all the samples of a class are averaged in the second method. The averaged wavelet packet coefficients are recognized by a RBF network. The proposed work tested on three face databases such as Olivetti-Oracle Research Lab (ORL), Japanese Female Facial Expression (JAFFE) and Essexface database. The proposed methods result in dimensionality reduction, low computational complexity and provide better recognition rates. The computational complexity is low as the dimensionality of the input pattern is reduced.展开更多
The objective of Ibis paper is to establish precise characterizations of scaling functions which are orthonormal or fundamental.A criterion for the corresponding wavelets is also given.
In this paper,an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material(FGM)using stationary wavelet transform(SWT)and neural network(NN).Material propert...In this paper,an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material(FGM)using stationary wavelet transform(SWT)and neural network(NN).Material properties of the structure vary along the thickness of beam elements by the power law of volumn distribution.Cracks are assumed to be open and are modeled by double massless springs with stiffness calculated from their depth.The dynamic stiffness method(DSM)is developed to calculate the mode shapes of a cracked frame structure based on shape functions obtained as a general solution of vibration in multiple cracked FGM Timoshenko beams.The SWT of mode shapes is examined for localization of potential cracks in the frame structure and utilized as the input data of NN for crack depth identification.The integrated procedure proposed is shown to be very effective for accurately assessing crack locations and depths in FGM structures,even with noisy measured mode shapes and a limited amount of measured data.展开更多
基金supported by the‘Pioneer’and‘Leading Goose’R&D Program of Zhejiang(Grant No.2023C02018)Zhejiang Provincial Natural Science Foundation of China(Grant No.LTGN23D010002)+2 种基金National Natural Science Foundation of China(Grant No.42371385)Funds of the Natural Science Foundation of Hangzhou(Grant No.2024SZRYBD010001)Nanxun Scholars Program of ZJWEU(Grant No.RC2022010755).
文摘Plant diseases are a major threat that can severely impact the production of agriculture and forestry.This can lead to the disruption of ecosystem functions and health.With its ability to capture continuous narrow-band spectra,hyperspectral technology has become a crucial tool to monitor crop diseases using remote sensing.However,existing continuous wavelet analysis(CWA)methods suffer from feature redundancy issues,while the continuous wavelet projection algorithm(CWPA),an optimization approach for feature selection,has not been fully validated to monitor plant diseases.This study utilized rice bacterial leaf blight(BLB)as an example by evaluating the performance of four wavelet basis functions-Gaussian2,Mexican hat,Meyer,andMorlet-within theCWAandCWPAframeworks.Additionally,the classification models were constructed using the k-nearest neighbors(KNN),randomforest(RF),and Naïve Bayes(NB)algorithms.The results showed the following:(1)Compared to traditional CWA,CWPA significantly reduced the number of required features.Under the CWPA framework,almost all the model combinations achieved maximum classification accuracy with only one feature.In contrast,the CWA framework required three to seven features.(2)Thechoice of wavelet basis functions markedly affected the performance of themodel.Of the four functions tested,the Meyer wavelet demonstrated the best overall performance in both the CWPA and CWA frameworks.(3)Under theCWPAframework,theMeyer-KNNandMeyer-NBcombinations achieved the highest overall accuracy of 93.75%using just one feature.In contrast,under the CWA framework,the CWA-RF combination achieved comparable accuracy(93.75%)but required six features.This study verified the technical advantages of CWPA for monitoring crop diseases,identified an optimal wavelet basis function selection scheme,and provided reliable technical support to precisely monitor BLB in rice(Oryza sativa).Moreover,the proposed methodological framework offers a scalable approach for the early diagnosis and assessment of plant stress,which can contribute to improved accuracy and timeliness when plant stress is monitored.
文摘Cardiovascular diseases are the world’s leading cause of death;therefore cardiac health of the human heart has been a fascinating topic for decades.The electrocardiogram(ECG)signal is a comprehensive non-invasive method for determining cardiac health.Various health practitioners use the ECG signal to ascertain critical information about the human heart.In this article,swarm intelligence approaches are used in the biomedical signal processing sector to enhance adaptive hybrid filters and empirical wavelet transforms(EWTs).At first,the white Gaussian noise is added to the input ECG signal and then applied to the EWT.The ECG signals are denoised by the proposed adaptive hybrid filter.The honey badge optimization(HBO)algorithm is utilized to optimize the EWT window function and adaptive hybrid filter weight parameters.The proposed approach is simulated by MATLAB 2018a using the MIT-BIH dataset with white Gaussian,electromyogram and electrode motion artifact noises.A comparison of the HBO approach with recursive least square-based adaptive filter,multichannel least means square,and discrete wavelet transform methods has been done in order to show the efficiency of the proposed adaptive hybrid filter.The experimental results show that the HBO approach supported by EWT and adaptive hybrid filter can be employed efficiently for cardiovascular signal denoising.
基金supported by the Major Basic Research Development Program of China (973 Project No. 2007CB209608)
文摘Phase spectrum estimation of the seismic wavelet is an important issue in high-resolution seismic data processing and interpretation. On the basis of two patterns of constant-phase rotation and root transform for wavelet phase spectrum variation, we introduce six sparse criteria, including Lu’s improved kurtosis criterion, the parsimony criterion, exponential transform criterion, Sech criterion, Cauchy criterion, and the modified Cauchy criterion, to phase spectrum estimation of the seismic wavelet, obtaining an equivalent effect to the kurtosis criterion. Through numerical experiments, we find that when the reflectivity is not a sparse sequence, the estimated phase spectrum of the seismic wavelet based on the criterion function will deviate from the true value. In order to eliminate the influence of non-sparse reflectivity series in a single trace, we apply the method to the multi-trace seismogram, improving the accuracy of seismic wavelet phase spectrum estimation.
基金Supported by the National Natural Science Founda-tion of China (49771060)
文摘The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal＇ s instantaneous amplitude and period.
基金Project supported by the National Natural Sciences Foundation of China(No.10432030).
文摘A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. With good features in treating singularities, Haar series solution converges rapidly for arbitrary distributions, especially for the case where the material properties change rapidly in some regions. Through numerical examples the influences of the ratio of material constants on the top and bottom surfaces and different material gradient distributions on the structural response of the plate to mechanical stimuli are studied.
基金supported by the National Natural Science Foundation of China (Nos.41374023,41131067,41474019)the National 973 Project of China (No.2013CB733302)+2 种基金the China Postdoctoral Science Foundation (No.2016M602301)the Key Laboratory of Geospace Envi-ronment and Geodesy,Ministry of Education,Wuhan University (No.15-02-08)the State Scholarship Fund from Chinese Scholarship Council (No.201306270014)
文摘The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.
基金the National Natural Science Foundation of China (50677014)Hunan Provincial Natural Science Foundation of China (06JJ50114).
文摘In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a novel steganographic method based on wavelet and modulus function is presented. First, an image is divided into blocks of prescribed size, and every block is decomposed into one-level wavelet. Then, the capacity of the hidden secret data is decided with the number of wavelet coefficients of larger magnitude. Finally, secret information is embedded by steganography based on modulus function. From the experimental results, the proposed method hides much more information and maintains a good visual quality of stego-image. Besides, the embedded data can be extracted from the stego-image without referencing the original image.
文摘In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression.
文摘Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When N = 2(k-1) and N = 2k, the unified analytic constructions of orthogonal wavelet filters are put forward, respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.
文摘The relations between Gaussian function and Γ function is revealed first at one dimensional situation. Then, the Fourier transformation of n dimensional Gaussian function is deduced by a lemma. Following the train of thought in one dimensional situation, the relation between n dimensional Gaussian function and Γ function is given. By these, the possibility of arbitrary derivative of an n dimensional Gaussian function being a mother wavelet is indicated. The result will take some enlightening role in exploring the internal relations between Gaussian function and Γ function as well as in finding high dimensional mother wavelets.
基金theNationalNaturalScienceFoundationofChina (No .50 40 90 0 8)
文摘Multiresolution analysis of wavelet theory can give an effective way to describe the information at various levels of approximations or different resolutions, based on spline wavelet analysis,so weight function is orthonormally projected onto a sequence of closed spline subspaces, and is viewed at various levels of approximations or different resolutions. Now, the useful new way to research weight function is found, and the numerical result is given.
文摘Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined by finite sets of parameters. Application to compression of fractal functions are also discussed.
文摘Over the past decade, wavelets provided a powerful and flexible set of tools for handling fundamental problems in science and engineering. Wavelet analyses are being used for solving problems in different engineering areas like audio de-noising, signal compression, object detection, image decomposition, speech recognition etc. Wavelet analysis employs orthonormal as well as non-orthonornal functions. This research investigates the effectiveness of wavelet analysis in detecting defects in underground steel pipe networks. Continuous Wavelet Transforms （CWT） has been performed on the received signals of cylindrical guided waves. Cylindrical Guided waves are generated and propagated through the pipe wall boundaries in a pitch-catch system. Piezo-electric transducers are used to generate as well as receive guided waves. Several mother wavelet functions such as Daubechies, Symlet, Coiflet and Meyer have been used for the Continuous Wavelet Transform to investigate the most suitable function for defect detection. This research also investigates the effect of surrounding soil on wavelet transforms for different mother wavelet functions.
基金Foundation items:the National Development Programming of Key Fundamental Researches of China(G1999022103)Planed Item for Distinguished Teacher Invested by Minisny of Education PRC
文摘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.
文摘We derive the conditions for the existence of the unique solution of the two scale integral equation and the form of the solution, according to the method of the construction of the dyadic scale function. We give the construction of the dyadic wavelet and its necessary and sufficient condition. As an application, we also develop a pyramid algorithm of the dyadic wavelet decomposition.
基金National Nature Science Foundation of China (49974021).
文摘A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initial model be-ing taken, a generalized least-squares inversion procedure is gradually carried out for receiver function from low to high scale, with the inversion result for low order receiver function as the initial model for high order. A neighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradu-ally focus at the global minimum by introducing high scale information of receiver function. With the gradual ad-dition of high wave-number to smooth background velocity structure, wavelet transformation can keep the inver-sion result converge to the global minimum, reduce to certain extent the dependence of inversion result on the initial model, overcome the nonuniqueness of generalized least-squares inversion, and obtain reliable crustal and upper mantle velocity with high resolution.
文摘Temporal activity patterns in animals emerge from complex interactions between choices made by organisms as responses to biotic interactions and challenges posed by external factors. Temporal activity pattern is an inherently continuous process, even being recorded as a time series. The discreteness of the data set is clearly due to data-acquisition limitations rather than a true underlying discrete nature of the phenomenon itself. Therefore, curves are a natural representation for high-frequency data. Here, we fully model temporal activity data as curves integrating wavelets and functional data analysis, allowing for testing hypotheses based on curves rather than on scalar and vector-valued data. Temporal activity data were obtained experimentally for males and females of a small-bodied marsupial and modelled as wavelets with independent and identically distributed errors and dependent errors. The null hypothesis of no difference in temporal activity pattern between male and female curves was tested with functional analysis of variance (FANOVA). The null hypothesis was rejected by FANOVA and we discussed the differences in temporal activity pattern curves between males and females in terms of ecological and life-history attributes of the reference species. We also performed numerical analysis that shed light on the regularity properties of the wavelet bases used and the thresholding parameters.
文摘An efficient face recognition system with face image representation using averaged wavelet packet coefficients, compact and meaningful feature vectors dimensional reduction and recognition using radial basis function (RBF) neural network is presented. The face images are decomposed by 2-level two-dimensional (2-D) wavelet packet transformation. The wavelet packet coefficients obtained from the wavelet packet transformation are averaged using two different proposed methods. In the first method, wavelet packet coefficients of individual samples of a class are averaged then decomposed. The wavelet packet coefficients of all the samples of a class are averaged in the second method. The averaged wavelet packet coefficients are recognized by a RBF network. The proposed work tested on three face databases such as Olivetti-Oracle Research Lab (ORL), Japanese Female Facial Expression (JAFFE) and Essexface database. The proposed methods result in dimensionality reduction, low computational complexity and provide better recognition rates. The computational complexity is low as the dimensionality of the input pattern is reduced.
基金NSF Grant #DMS-89-01345ARO Contract DAAL 03-90-G-0091
文摘The objective of Ibis paper is to establish precise characterizations of scaling functions which are orthonormal or fundamental.A criterion for the corresponding wavelets is also given.
基金Project supported by the Vietnam National Foundation for Science and Technology Development(No.107.02-2017.301)。
文摘In this paper,an integrated procedure is proposed to identify cracks in a portal framed structure made of functionally graded material(FGM)using stationary wavelet transform(SWT)and neural network(NN).Material properties of the structure vary along the thickness of beam elements by the power law of volumn distribution.Cracks are assumed to be open and are modeled by double massless springs with stiffness calculated from their depth.The dynamic stiffness method(DSM)is developed to calculate the mode shapes of a cracked frame structure based on shape functions obtained as a general solution of vibration in multiple cracked FGM Timoshenko beams.The SWT of mode shapes is examined for localization of potential cracks in the frame structure and utilized as the input data of NN for crack depth identification.The integrated procedure proposed is shown to be very effective for accurately assessing crack locations and depths in FGM structures,even with noisy measured mode shapes and a limited amount of measured data.
