As wavelet basis in wavelet analysis is neither arbitrary nor unique,the same signal dealing with different wavelet bases will generate different results.Therefore,how to construct a wavelet basis suitable for the cha...As wavelet basis in wavelet analysis is neither arbitrary nor unique,the same signal dealing with different wavelet bases will generate different results.Therefore,how to construct a wavelet basis suitable for the characteristics of the analyzed signal and solve its algorithm and realization is a fundamental problem which perplexed many researchers.To solve these problems,in accordance with the basic features of the measured millisecond blast vibration signal,a new wavelet basis construction method based on the separation blast vibration signal is proposed,and the feasibility of this method is verified by comparing the practical effect of the newly constructed wavelet with other known wavelets in signal processing.展开更多
In the paper by using the spline wavelet basis to constructr the approximate inertial manifold, we study the longtime behavior of perturbed perodic KdV equation.
In this paper, we show the construction of orthogonal wavelet basis on the interval [0, 1],using compactly supportted Daubechies function. Forwardly, we suggest a kind of method to deal with the differential operator ...In this paper, we show the construction of orthogonal wavelet basis on the interval [0, 1],using compactly supportted Daubechies function. Forwardly, we suggest a kind of method to deal with the differential operator in view of numerical analysis and derive the appoximation algorithm of wavelet ba-sis and differential operator, which affects on the basis, to functions belonging to L2 [0, 1 ]. Numerical computation indicate the stability and effectiveness of the algorithm.展开更多
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
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
Due to the disturbances arising from the coherence of reflected waves and from echo noise,problems such as limitations,instability and poor accuracy exist with the current quantitative analysis methods.According to th...Due to the disturbances arising from the coherence of reflected waves and from echo noise,problems such as limitations,instability and poor accuracy exist with the current quantitative analysis methods.According to the intrinsic features of GPR signals and wavelet time–frequency analysis,an optimal wavelet basis named GPR3.3 wavelet is constructed via an improved biorthogonal wavelet construction method to quantitatively analyse the GPR signal.A new quantitative analysis method based on the biorthogonal wavelet(the QAGBW method)is proposed and applied in the analysis of analogue and measured signals.The results show that compared with the Bayesian frequency-domain blind deconvolution and with existing wavelet bases,the QAGBW method based on optimal wavelet can limit the disturbance from factors such as the coherence of reflected waves and echo noise,improve the quantitative analytical precision of the GPR signal,and match the minimum thickness for quantitative analysis with the vertical resolution of GPR detection.展开更多
Tomographic synthetic aperture radar(TomoSAR)imaging exploits the antenna array measurements taken at different elevation aperture to recover the reflectivity function along the elevation direction.In these years,for ...Tomographic synthetic aperture radar(TomoSAR)imaging exploits the antenna array measurements taken at different elevation aperture to recover the reflectivity function along the elevation direction.In these years,for the sparse elevation distribution,compressive sensing(CS)is a developed favorable technique for the high-resolution elevation reconstruction in TomoSAR by solving an L_(1) regularization problem.However,because the elevation distribution in the forested area is nonsparse,if we want to use CS in the recovery,some basis,such as wavelet,should be exploited in the sparse L_(1/2) representation of the elevation reflectivity function.This paper presents a novel wavelet-based L_(2) regularization CS-TomoSAR imaging method of the forested area.In the proposed method,we first construct a wavelet basis,which can sparsely represent the elevation reflectivity function of the forested area,and then reconstruct the elevation distribution by using the L_(1/2) regularization technique.Compared to the wavelet-based L_(1) regularization TomoSAR imaging,the proposed method can improve the elevation recovered quality efficiently.展开更多
We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warp...We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warped wavelet basis. We investigate the properties of this new basis and evaluate its asymptotic performance by determining an upper bound of the mean integrated squared error under different dependence structures. We prove that it attains a sharp rate of convergence for a wide class of unknown regression functions.展开更多
Suppose M and N are two r×r and s×s dilation matrices,respectively.LetΓM andΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-T Zr/Zr and N-T Zs/Zs,respectively....Suppose M and N are two r×r and s×s dilation matrices,respectively.LetΓM andΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-T Zr/Zr and N-T Zs/Zs,respectively.Two methods for constructing nonseparable Ω-filter banks from M-filter banks and N-filter banks are presented,where Ω is a（r＋s） ×（r＋s） dilation matrix such that one of its complete sets of representatives of distinct cosets of the quotient groups Ω-T Zr＋s/Zr＋s areΓΩ={[γT h,ζ T q] T：γh∈ΓM,ζq∈ΓN}.Specially,Ω can be [MΘ0N],whereΘis a r×s integer matrix with M-1Θbeing also an integer matrix.Moreover,if the constructed filter bank satisfies Lawton＇s condition,which can be easy to verify,then it generates an orthonormal nonseparable Ω-wavelet basis for L2（Rr＋s）.Properties,including Lawton＇s condition,vanishing moments and regularity of the new Ω-filter banks or new Ω-wavelet basis are discussed then.Finally,a class of nonseparable Ω-wavelet basis for L2（Rr＋1） are constructed and three other examples are given to illustrate the results.In particular,when M=N=2,all results obtained in this paper appeared in[1].展开更多
In the acoustic detection process of buried non-metallic pipelines,the echo signal is often interfered by a large amount of noise,which makes it extremely difficult to effectively extract useful signals.An denoising a...In the acoustic detection process of buried non-metallic pipelines,the echo signal is often interfered by a large amount of noise,which makes it extremely difficult to effectively extract useful signals.An denoising algorithm based on empirical mode decomposition(EMD)and wavelet thresholding was proposed.This method fully considered the nonlinear and non-stationary characteristics of the echo signal,making the denoising effect more significant.Its feasibility and effectiveness were verified through numerical simulation.When the input SNR(SNRin)is between-10 dB and 10 dB,the output SNR(SNRout)of the combined denoising algorithm increases by 12.0%-34.1%compared to the wavelet thresholding method and by 19.60%-56.8%compared to the EMD denoising method.Additionally,the RMSE of the combined denoising algorithm decreases by 18.1%-48.0%compared to the wavelet thresholding method and by 22.1%-48.8%compared to the EMD denoising method.These results indicated that this joint denoising algorithm could not only effectively reduce noise interference,but also significantly improve the positioning accuracy of acoustic detection.The research results could provide technical support for denoising the echo signals of buried non-metallic pipelines,which was conducive to improving the acoustic detection and positioning accuracy of underground non-metallic pipelines.展开更多
Using wavelets, the vibration signal of a certain mine hoist gear box was analyzed. By multiple comparison analysis, the rational wavelet basis function was determined. Fault characteristic frequencies of hoist gear b...Using wavelets, the vibration signal of a certain mine hoist gear box was analyzed. By multiple comparison analysis, the rational wavelet basis function was determined. Fault characteristic frequencies of hoist gear box were identified. The research indicates that the hoist＇s fault information is non-stationary, and non-stationary signal is clearly extracted by using db20 wavelet as basis function. The db20 wavelet is the proper wavelet base for vibration signal analysis of the hoist gear box.展开更多
An improved wavelet packet domain least mean square （IWPD-LMS） based adaptive muhiuser detection algorithm is proposed. The algorithm employs the wavelet packet transform to rewhiten the input data, and chooses the ...An improved wavelet packet domain least mean square （IWPD-LMS） based adaptive muhiuser detection algorithm is proposed. The algorithm employs the wavelet packet transform to rewhiten the input data, and chooses the best wavelet packet basis according to a novel convergence contribution function rather than the conventional Shannon entropy. The theoretic analyses show that the inadequacy of the eigenvalue spread of the tap-input correlation matrix is ameliorated, thus the convergence performance is improved greatly. The simulation result of convergence performance and bit error rate（BER） performance as a function of the signal power to noise power ratio（SNR） are presented finally to prove the validity of the proposed algorithm.展开更多
Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples.In this paper,we shall construct Riesz wavelet associated with dual pseudo splines.Furthermore,we use dual pseudo sp...Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples.In this paper,we shall construct Riesz wavelet associated with dual pseudo splines.Furthermore,we use dual pseudo splines to construct tight frame systems with desired approximation order by applying the unitary extension principle.展开更多
Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.
Given a multiresolution analysis of multidimension, we construct pre-wavelets and a Rieszwavelet basis under some assumptions on the scale function. Example are provided.
We construct an unconditional basis in the Banach space Lp(Ω, ρ) for p ＞ 1 by using the refinement equation and the basic operation of translation and scale, where Ω is a compact subset in Rn. We also give an algo...We construct an unconditional basis in the Banach space Lp(Ω, ρ) for p ＞ 1 by using the refinement equation and the basic operation of translation and scale, where Ω is a compact subset in Rn. We also give an algorithm of how to construct an unconditional basis in Lp(Ω, ρ). At the end of this paper, we give the characterization of the functions in Lp(Ω, ρ) by using the wavelet coefficients.展开更多
基金Projects(51078043,51278071,51308072)supported by the National Natural Science Foundation of China
文摘As wavelet basis in wavelet analysis is neither arbitrary nor unique,the same signal dealing with different wavelet bases will generate different results.Therefore,how to construct a wavelet basis suitable for the characteristics of the analyzed signal and solve its algorithm and realization is a fundamental problem which perplexed many researchers.To solve these problems,in accordance with the basic features of the measured millisecond blast vibration signal,a new wavelet basis construction method based on the separation blast vibration signal is proposed,and the feasibility of this method is verified by comparing the practical effect of the newly constructed wavelet with other known wavelets in signal processing.
文摘In the paper by using the spline wavelet basis to constructr the approximate inertial manifold, we study the longtime behavior of perturbed perodic KdV equation.
文摘In this paper, we show the construction of orthogonal wavelet basis on the interval [0, 1],using compactly supportted Daubechies function. Forwardly, we suggest a kind of method to deal with the differential operator in view of numerical analysis and derive the appoximation algorithm of wavelet ba-sis and differential operator, which affects on the basis, to functions belonging to L2 [0, 1 ]. Numerical computation indicate the stability and effectiveness of the algorithm.
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.
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Projects(51678071,51278071)supported by the National Natural Science Foundation of ChinaProjects(14KC06,CX2015BS02)supported by Changsha University of Science&Technology,China
文摘Due to the disturbances arising from the coherence of reflected waves and from echo noise,problems such as limitations,instability and poor accuracy exist with the current quantitative analysis methods.According to the intrinsic features of GPR signals and wavelet time–frequency analysis,an optimal wavelet basis named GPR3.3 wavelet is constructed via an improved biorthogonal wavelet construction method to quantitatively analyse the GPR signal.A new quantitative analysis method based on the biorthogonal wavelet(the QAGBW method)is proposed and applied in the analysis of analogue and measured signals.The results show that compared with the Bayesian frequency-domain blind deconvolution and with existing wavelet bases,the QAGBW method based on optimal wavelet can limit the disturbance from factors such as the coherence of reflected waves and echo noise,improve the quantitative analytical precision of the GPR signal,and match the minimum thickness for quantitative analysis with the vertical resolution of GPR detection.
基金This work was supported by the Fundamental Research Funds for the Central Universities(NE2020004)the National Natural Science Foundation of China(61901213)+3 种基金the Natural Science Foundation of Jiangsu Province(BK20190397)the Aeronautical Science Foundation of China(201920052001)the Young Science and Technology Talent Support Project of Jiangsu Science and Technology Associationthe Foundation of Graduate Innovation Center in Nanjing University of Aeronautics and Astronautics(kfjj20200419).
文摘Tomographic synthetic aperture radar(TomoSAR)imaging exploits the antenna array measurements taken at different elevation aperture to recover the reflectivity function along the elevation direction.In these years,for the sparse elevation distribution,compressive sensing(CS)is a developed favorable technique for the high-resolution elevation reconstruction in TomoSAR by solving an L_(1) regularization problem.However,because the elevation distribution in the forested area is nonsparse,if we want to use CS in the recovery,some basis,such as wavelet,should be exploited in the sparse L_(1/2) representation of the elevation reflectivity function.This paper presents a novel wavelet-based L_(2) regularization CS-TomoSAR imaging method of the forested area.In the proposed method,we first construct a wavelet basis,which can sparsely represent the elevation reflectivity function of the forested area,and then reconstruct the elevation distribution by using the L_(1/2) regularization technique.Compared to the wavelet-based L_(1) regularization TomoSAR imaging,the proposed method can improve the elevation recovered quality efficiently.
文摘We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warped wavelet basis. We investigate the properties of this new basis and evaluate its asymptotic performance by determining an upper bound of the mean integrated squared error under different dependence structures. We prove that it attains a sharp rate of convergence for a wide class of unknown regression functions.
基金Supported by the National Natural Science Foundation of China(11071152)the Natural Science Foundation of Guangdong Province(10151503101000025)
文摘Suppose M and N are two r×r and s×s dilation matrices,respectively.LetΓM andΓN represent the complete sets of representatives of distinct cosets of the quotient groups M-T Zr/Zr and N-T Zs/Zs,respectively.Two methods for constructing nonseparable Ω-filter banks from M-filter banks and N-filter banks are presented,where Ω is a（r＋s） ×（r＋s） dilation matrix such that one of its complete sets of representatives of distinct cosets of the quotient groups Ω-T Zr＋s/Zr＋s areΓΩ={[γT h,ζ T q] T：γh∈ΓM,ζq∈ΓN}.Specially,Ω can be [MΘ0N],whereΘis a r×s integer matrix with M-1Θbeing also an integer matrix.Moreover,if the constructed filter bank satisfies Lawton＇s condition,which can be easy to verify,then it generates an orthonormal nonseparable Ω-wavelet basis for L2（Rr＋s）.Properties,including Lawton＇s condition,vanishing moments and regularity of the new Ω-filter banks or new Ω-wavelet basis are discussed then.Finally,a class of nonseparable Ω-wavelet basis for L2（Rr＋1） are constructed and three other examples are given to illustrate the results.In particular,when M=N=2,all results obtained in this paper appeared in[1].
基金supported by Nanchong Southwest Petroleum University Science and Technology Strategic Cooperation Project(Nos.23XNSYSX0022,23XNSYSX0026)Provincial Science and Technology Plan Project(No.2023ZHCG0020)Southwest Petroleum University Natural Science“Sailing Plan”Project(No.2023QHZ003)。
文摘In the acoustic detection process of buried non-metallic pipelines,the echo signal is often interfered by a large amount of noise,which makes it extremely difficult to effectively extract useful signals.An denoising algorithm based on empirical mode decomposition(EMD)and wavelet thresholding was proposed.This method fully considered the nonlinear and non-stationary characteristics of the echo signal,making the denoising effect more significant.Its feasibility and effectiveness were verified through numerical simulation.When the input SNR(SNRin)is between-10 dB and 10 dB,the output SNR(SNRout)of the combined denoising algorithm increases by 12.0%-34.1%compared to the wavelet thresholding method and by 19.60%-56.8%compared to the EMD denoising method.Additionally,the RMSE of the combined denoising algorithm decreases by 18.1%-48.0%compared to the wavelet thresholding method and by 22.1%-48.8%compared to the EMD denoising method.These results indicated that this joint denoising algorithm could not only effectively reduce noise interference,but also significantly improve the positioning accuracy of acoustic detection.The research results could provide technical support for denoising the echo signals of buried non-metallic pipelines,which was conducive to improving the acoustic detection and positioning accuracy of underground non-metallic pipelines.
文摘Using wavelets, the vibration signal of a certain mine hoist gear box was analyzed. By multiple comparison analysis, the rational wavelet basis function was determined. Fault characteristic frequencies of hoist gear box were identified. The research indicates that the hoist＇s fault information is non-stationary, and non-stationary signal is clearly extracted by using db20 wavelet as basis function. The db20 wavelet is the proper wavelet base for vibration signal analysis of the hoist gear box.
基金Sponsored by the National"863"Program Projects (2007AA012293)
文摘An improved wavelet packet domain least mean square （IWPD-LMS） based adaptive muhiuser detection algorithm is proposed. The algorithm employs the wavelet packet transform to rewhiten the input data, and chooses the best wavelet packet basis according to a novel convergence contribution function rather than the conventional Shannon entropy. The theoretic analyses show that the inadequacy of the eigenvalue spread of the tap-input correlation matrix is ameliorated, thus the convergence performance is improved greatly. The simulation result of convergence performance and bit error rate（BER） performance as a function of the signal power to noise power ratio（SNR） are presented finally to prove the validity of the proposed algorithm.
基金supported by National Natural Science Foundation of China (Grant Nos.10771190,10971189)Natural Science Foundation of China of Zhejiang Province (Grant No. Y6090091)
文摘Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples.In this paper,we shall construct Riesz wavelet associated with dual pseudo splines.Furthermore,we use dual pseudo splines to construct tight frame systems with desired approximation order by applying the unitary extension principle.
文摘Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.
文摘Given a multiresolution analysis of multidimension, we construct pre-wavelets and a Rieszwavelet basis under some assumptions on the scale function. Example are provided.
文摘We construct an unconditional basis in the Banach space Lp(Ω, ρ) for p ＞ 1 by using the refinement equation and the basic operation of translation and scale, where Ω is a compact subset in Rn. We also give an algorithm of how to construct an unconditional basis in Lp(Ω, ρ). At the end of this paper, we give the characterization of the functions in Lp(Ω, ρ) by using the wavelet coefficients.
