The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secur...The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secure communications.So,this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets.The Caputo fractional Rössler attractor model is simulated into two categories,(i)Asymmetric and(ii)Symmetric.The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of the Caputo fractional Rössler attractor model,depicting each computation in graphs and tables to analyze how fractional order affects the model’s dynamics.Approximate solutions obtained through the proposed scheme for integer order are well comparable with the fourth-order Runge-Kutta method.Also,the stability analyses of the considered model are discussed for different equilibrium points.Various fractional orders are considered while performing numerical simulations for the Caputo fractional Rössler attractor model by using Mathematica.The suggested approach can solve another non-linear fractional model due to its straightforward implementation.展开更多
In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study h...In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study here the application of that method to the detection of edge of a function. Mathieu et al. proposed the CRONE detector for a detection of an edge of an image. For a function without noise, we note that the CRONE detector is expressed as the Riesz fractional derivative (fD) of the derivative. We study here the application of the mollification to the calculation of the Riesz fD of the derivative for a data involving noise, and compare the results with the results obtained by our method of applying simple derivative to mollified data.展开更多
An Euler wavelets method is proposed to solve a class of nonlinear variable order fractional differential equations in this paper.The properties of Euler wavelets and their operational matrix together with a family of...An Euler wavelets method is proposed to solve a class of nonlinear variable order fractional differential equations in this paper.The properties of Euler wavelets and their operational matrix together with a family of piecewise functions are first presented.Then they are utilized to reduce the problem to the solution of a nonlinear system of algebraic equations.And the convergence of the Euler wavelets basis is given.The method is computationally attractive and some numerical examples are provided to illustrate its high accuracy.展开更多
As process technology development,model order reduction( MOR) has been regarded as a useful tool in analysis of on-chip interconnects. We propose a weighted self-adaptive threshold wavelet interpolation MOR method on ...As process technology development,model order reduction( MOR) has been regarded as a useful tool in analysis of on-chip interconnects. We propose a weighted self-adaptive threshold wavelet interpolation MOR method on account of Krylov subspace techniques. The interpolation points are selected by Haar wavelet using weighted self-adaptive threshold methods dynamically. Through the analyses of different types of circuits in very large scale integration( VLSI),the results show that the method proposed in this paper can be more accurate and efficient than Krylov subspace method of multi-shift expansion point using Haar wavelet that are no weighted self-adaptive threshold application in interest frequency range,and more accurate than Krylov subspace method of multi-shift expansion point based on the uniform interpolation point.展开更多
An attempt has been made to apply the wavelet methodology for the study of the results of the chaotic behavior of multiparticle production in relativistic heavy ion collisions. We reviewed the data that describes the ...An attempt has been made to apply the wavelet methodology for the study of the results of the chaotic behavior of multiparticle production in relativistic heavy ion collisions. We reviewed the data that describes the collisions of relativistic heavy ion for the case η-space in 1-D phase space of variable. We compared the experimental data and UrQMD data using wavelet coherency. We discussed the results of the comparison.展开更多
Machine learning is an integral technology many people utilize in all areas of human life. It is pervasive in modern living worldwide, and has multiple usages. One application is image classification, embraced across ...Machine learning is an integral technology many people utilize in all areas of human life. It is pervasive in modern living worldwide, and has multiple usages. One application is image classification, embraced across many spheres of influence such as business, finance, medicine, etc. to enhance produces, causes, efficiency, etc. This need for more accurate, detail-oriented classification increases the need for modifications, adaptations, and innovations to Deep Learning Algorithms. This article used Convolutional Neural Networks (CNN) to classify scenes in the CIFAR-10 database, and detect emotions in the KDEF database. The proposed method converted the data to the wavelet domain to attain greater accuracy and comparable efficiency to the spatial domain processing. By dividing image data into subbands, important feature learning occurred over differing low to high frequencies. The combination of the learned low and high frequency features, and processing the fused feature mapping resulted in an advance in the detection accuracy. Comparing the proposed methods to spatial domain CNN and Stacked Denoising Autoencoder (SDA), experimental findings revealed a substantial increase in accuracy.展开更多
Land cover changes (LCC) are an important component of Global Change. LCC can be described not only by its occurrence, but also by the land cover replacement, causal agent and change duration or recuperation. Nowadays...Land cover changes (LCC) are an important component of Global Change. LCC can be described not only by its occurrence, but also by the land cover replacement, causal agent and change duration or recuperation. Nowadays, remote sensing offers the opportunity to assemble reliable time series, however this fails to make a characterization of LCC since the series represents dynamics due to the combination of several processes occurring simultaneously. In this article we proposed an approach to the study of LCC using wavelet transform (WT) and MODIS vegetation time series. Through this work we have demonstrated the capacity of this tool in order to recognize and characterize four different LLC documented in scientific publications, presenting the results divided in frequency scales as interannual, seasonal and rapid changes. The information decomposed in frequency allows the interpretation of each involved process without the interference of others. The uses of WT in an image time series give us the possibility of joining temporal and spatial dimension in a single raster. Layers generated with WT might be used to pattern recognition in LCC and to improve an image classification.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
This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. The...This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.展开更多
The wavelet adapted to the fabric texture can be developed from the orthogonal and normal series which are selected randomly by means of Monte Carlo method and op timized by adding certain constraint conditions.Then t...The wavelet adapted to the fabric texture can be developed from the orthogonal and normal series which are selected randomly by means of Monte Carlo method and op timized by adding certain constraint conditions.Then the fabric image can be decomposed into the subimages by the adaptive wavelet transform and the horizontal and vertical texture information will be perfectly contained in the subimages. Therefore this method can be effectively used for the automatic inspection of the fabric defects.展开更多
This article concerns the application of wavelet techniques on molecular surfaces constituted of four-sided patches. The Polarizable Continuum Model, which is governed by the Poisson-Boltzmann equation, is treated by ...This article concerns the application of wavelet techniques on molecular surfaces constituted of four-sided patches. The Polarizable Continuum Model, which is governed by the Poisson-Boltzmann equation, is treated by means of boundary integral equations. The media inside and outside the molecular surface consist respectively of the solute and the solvent. For a given electrically charged molecule, the principal unknown is the electrostatic solvation energy when the permittivity is specified. The wavelet basis functions are constructed on the unit square which are subsequently mapped onto the patches that are assumed to be isotropically shaped and to admit similar surface areas. The initial transmission problem is recast as an integral equation in term of both the single and the double layers. Domain decomposition preconditioner serves as acceleration of the linear solver of the single layer which is badly conditioned.展开更多
This document presents a framework for recognizing people by palm vein distribution analysis using cross-correlation based signatures to obtain descriptors. Haar wavelets are useful in reducing the number of features ...This document presents a framework for recognizing people by palm vein distribution analysis using cross-correlation based signatures to obtain descriptors. Haar wavelets are useful in reducing the number of features while maintaining high recognition rates. This experiment achieved 97.5% of individuals classified correctly with two levels of Haar wavelets. This study used twelve-version of RGB and NIR (near infrared) wavelength images per individual. One hundred people were studied;therefore 4,800 instances compose the complete database. A Multilayer Perceptron (MLP) was trained to improve the recognition rate in a k-fold cross-validation test with k = 10. Classification results using MLP neural network were obtained using Weka (open source machine learning software).展开更多
A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent pea...A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum （EPS）. Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average （ARMA） filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals＇ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice.展开更多
In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = ...In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.展开更多
This paper presents a novel method utilizing wavelets with particle swarm optimization(PSO)for medical image compression.Our method utilizes PSO to overcome the wavelets discontinuity which occurs when compressing ima...This paper presents a novel method utilizing wavelets with particle swarm optimization(PSO)for medical image compression.Our method utilizes PSO to overcome the wavelets discontinuity which occurs when compressing images using thresholding.It transfers images into subband details and approximations using a modified Haar wavelet(MHW),and then applies a threshold.PSO is applied for selecting a particle assigned to the threshold values for the subbands.Nine positions assigned to particles values are used to represent population.Every particle updates its position depending on the global best position(gbest)(for all details subband)and local best position(pbest)(for a subband).The fitness value is developed to terminate PSO when the difference between two local best(pbest)successors is smaller than a prescribe value.The experiments are applied on five different medical image types,i.e.,MRI,CT,and X-ray.Results show that the proposed algorithm can be more preferably to compress medical images than other existing wavelets techniques from peak signal to noise ratio(PSNR)and compression ratio(CR)points of views.展开更多
The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vec...The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.展开更多
In this paper, wavelet transform and entropy are evaluated using the mathematical analysis concepts of reflexibility, regularity and series obtention, these concepts remark the reason to make a selective reference fra...In this paper, wavelet transform and entropy are evaluated using the mathematical analysis concepts of reflexibility, regularity and series obtention, these concepts remark the reason to make a selective reference framework for power quality applications. With this idea the paper used the same treatment for the two algorithms (Multiresolution and Multiscale Entropy). The wavelet is denoted to have the most power full consistence to the light off the reflexibility, regularity and series obtention. The paper proposes a power quality technique namely MpqAT.展开更多
Air-gun arrays are used in marine-seismic exploration. Far-field wavelets in subsurface media represent the stacking of single air-gun ideal wavelets. We derived single air-gun ideal wavelets using near-field wavelets...Air-gun arrays are used in marine-seismic exploration. Far-field wavelets in subsurface media represent the stacking of single air-gun ideal wavelets. We derived single air-gun ideal wavelets using near-field wavelets recorded from near-field geophones and then synthesized them into far-field wavelets. This is critical for processing wavelets in marine- seismic exploration. For this purpose, several algorithms are currently used to decompose and synthesize wavelets in the time domain. If the traveltime of single air-gun wavelets is not an integral multiple of the sampling interval, the complex and error-prone resampling of the seismic signals using the time-domain method is necessary. Based on the relation between the frequency-domain phase and the time-domain time delay, we propose a method that first transforms the real near-field wavelet to the frequency domain via Fourier transforms; then, it decomposes it and composes the wavelet spectrum in the frequency domain, and then back transforms it to the time domain. Thus, the resampling problem is avoided and single air-gun wavelets and far-field wavelets can be reliably derived. The effect of ghost reflections is also considered, while decomposing the wavelet and removing the ghost reflections. Modeling and real data processing were used to demonstrate the feasibility of the proposed method.展开更多
A novel multiresolution approach to the discrimination of textures using wavelets is presented. The approach employs an overcomplete wavelet decomposition called wavelet frames, which gives the description of both tra...A novel multiresolution approach to the discrimination of textures using wavelets is presented. The approach employs an overcomplete wavelet decomposition called wavelet frames, which gives the description of both translation invariance and stability. In order to adapt to the quasi periodic property of textures, we propose the application of tree structured wavelet packet analysis. For discriminating efficiency, we develop a progressive texture discriminating algorithm, in which the discrimination process terminates once a suitably chosen discrimination criterion is met. Experiments show that with a minimal number of wavelet frame decompositions and iterations, our proposed approach could achieve a 100% correct discrimination rate on all the 12 texture types tested. That outperforms many of the existing approaches in terms of accuracy and computational efficiency, and thus it appears to be attractive for real time application involving texture based video/image classification.展开更多
基金"La derivada fraccional generalizada,nuevos resultados y aplicaciones a desigualdades integrales"Cod UIO-077-2024supported via funding from Prince Sattam bin Abdulaziz University project number(PSAU/2025/R/1446).
文摘The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secure communications.So,this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets.The Caputo fractional Rössler attractor model is simulated into two categories,(i)Asymmetric and(ii)Symmetric.The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of the Caputo fractional Rössler attractor model,depicting each computation in graphs and tables to analyze how fractional order affects the model’s dynamics.Approximate solutions obtained through the proposed scheme for integer order are well comparable with the fourth-order Runge-Kutta method.Also,the stability analyses of the considered model are discussed for different equilibrium points.Various fractional orders are considered while performing numerical simulations for the Caputo fractional Rössler attractor model by using Mathematica.The suggested approach can solve another non-linear fractional model due to its straightforward implementation.
文摘In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study here the application of that method to the detection of edge of a function. Mathieu et al. proposed the CRONE detector for a detection of an edge of an image. For a function without noise, we note that the CRONE detector is expressed as the Riesz fractional derivative (fD) of the derivative. We study here the application of the mollification to the calculation of the Riesz fD of the derivative for a data involving noise, and compare the results with the results obtained by our method of applying simple derivative to mollified data.
基金The authors are grateful to the editor,the associate editor and the anonymous reviewers for their constructive and helpful comments.This work was supported by the Zhejiang Provincial Natural Science Foundation of China(No.LY18A010026),the National Natural Science Foundation of China(No.11701304,11526117)Zhejiang Provincial Natural Science Foundation of China(No.LQ16A010006)+1 种基金the Natural Science Foundation of Ningbo City,China(No.2017A610143)the Natural Science Foundation of Ningbo City,China(2018A610195).
文摘An Euler wavelets method is proposed to solve a class of nonlinear variable order fractional differential equations in this paper.The properties of Euler wavelets and their operational matrix together with a family of piecewise functions are first presented.Then they are utilized to reduce the problem to the solution of a nonlinear system of algebraic equations.And the convergence of the Euler wavelets basis is given.The method is computationally attractive and some numerical examples are provided to illustrate its high accuracy.
基金Sponsored by the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.2016107)the China Postdoctoral Science Foundation(Grant No.2015M581447)
文摘As process technology development,model order reduction( MOR) has been regarded as a useful tool in analysis of on-chip interconnects. We propose a weighted self-adaptive threshold wavelet interpolation MOR method on account of Krylov subspace techniques. The interpolation points are selected by Haar wavelet using weighted self-adaptive threshold methods dynamically. Through the analyses of different types of circuits in very large scale integration( VLSI),the results show that the method proposed in this paper can be more accurate and efficient than Krylov subspace method of multi-shift expansion point using Haar wavelet that are no weighted self-adaptive threshold application in interest frequency range,and more accurate than Krylov subspace method of multi-shift expansion point based on the uniform interpolation point.
文摘An attempt has been made to apply the wavelet methodology for the study of the results of the chaotic behavior of multiparticle production in relativistic heavy ion collisions. We reviewed the data that describes the collisions of relativistic heavy ion for the case η-space in 1-D phase space of variable. We compared the experimental data and UrQMD data using wavelet coherency. We discussed the results of the comparison.
文摘Machine learning is an integral technology many people utilize in all areas of human life. It is pervasive in modern living worldwide, and has multiple usages. One application is image classification, embraced across many spheres of influence such as business, finance, medicine, etc. to enhance produces, causes, efficiency, etc. This need for more accurate, detail-oriented classification increases the need for modifications, adaptations, and innovations to Deep Learning Algorithms. This article used Convolutional Neural Networks (CNN) to classify scenes in the CIFAR-10 database, and detect emotions in the KDEF database. The proposed method converted the data to the wavelet domain to attain greater accuracy and comparable efficiency to the spatial domain processing. By dividing image data into subbands, important feature learning occurred over differing low to high frequencies. The combination of the learned low and high frequency features, and processing the fused feature mapping resulted in an advance in the detection accuracy. Comparing the proposed methods to spatial domain CNN and Stacked Denoising Autoencoder (SDA), experimental findings revealed a substantial increase in accuracy.
文摘Land cover changes (LCC) are an important component of Global Change. LCC can be described not only by its occurrence, but also by the land cover replacement, causal agent and change duration or recuperation. Nowadays, remote sensing offers the opportunity to assemble reliable time series, however this fails to make a characterization of LCC since the series represents dynamics due to the combination of several processes occurring simultaneously. In this article we proposed an approach to the study of LCC using wavelet transform (WT) and MODIS vegetation time series. Through this work we have demonstrated the capacity of this tool in order to recognize and characterize four different LLC documented in scientific publications, presenting the results divided in frequency scales as interannual, seasonal and rapid changes. The information decomposed in frequency allows the interpretation of each involved process without the interference of others. The uses of WT in an image time series give us the possibility of joining temporal and spatial dimension in a single raster. Layers generated with WT might be used to pattern recognition in LCC and to improve an image classification.
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.
基金supported by the Natural Science Foundation China(11126343)Guangxi Natural Science Foundation(2013GXNSFBA019010)+1 种基金supported by Natural Science Foundation China(11071152)Natural Science Foundation of Guangdong Province(10151503101000025,S2011010004511)
文摘This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.
基金the Research Fund for the Doctoral Program of Higher Education(No.99025508)
文摘The wavelet adapted to the fabric texture can be developed from the orthogonal and normal series which are selected randomly by means of Monte Carlo method and op timized by adding certain constraint conditions.Then the fabric image can be decomposed into the subimages by the adaptive wavelet transform and the horizontal and vertical texture information will be perfectly contained in the subimages. Therefore this method can be effectively used for the automatic inspection of the fabric defects.
文摘This article concerns the application of wavelet techniques on molecular surfaces constituted of four-sided patches. The Polarizable Continuum Model, which is governed by the Poisson-Boltzmann equation, is treated by means of boundary integral equations. The media inside and outside the molecular surface consist respectively of the solute and the solvent. For a given electrically charged molecule, the principal unknown is the electrostatic solvation energy when the permittivity is specified. The wavelet basis functions are constructed on the unit square which are subsequently mapped onto the patches that are assumed to be isotropically shaped and to admit similar surface areas. The initial transmission problem is recast as an integral equation in term of both the single and the double layers. Domain decomposition preconditioner serves as acceleration of the linear solver of the single layer which is badly conditioned.
文摘This document presents a framework for recognizing people by palm vein distribution analysis using cross-correlation based signatures to obtain descriptors. Haar wavelets are useful in reducing the number of features while maintaining high recognition rates. This experiment achieved 97.5% of individuals classified correctly with two levels of Haar wavelets. This study used twelve-version of RGB and NIR (near infrared) wavelength images per individual. One hundred people were studied;therefore 4,800 instances compose the complete database. A Multilayer Perceptron (MLP) was trained to improve the recognition rate in a k-fold cross-validation test with k = 10. Classification results using MLP neural network were obtained using Weka (open source machine learning software).
文摘A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum （EPS）. Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average （ARMA） filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals＇ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice.
文摘In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved.
基金funded by the University of Jeddah,Saudi Arabia,under Grant No.UJ-20-043-DR。
文摘This paper presents a novel method utilizing wavelets with particle swarm optimization(PSO)for medical image compression.Our method utilizes PSO to overcome the wavelets discontinuity which occurs when compressing images using thresholding.It transfers images into subband details and approximations using a modified Haar wavelet(MHW),and then applies a threshold.PSO is applied for selecting a particle assigned to the threshold values for the subbands.Nine positions assigned to particles values are used to represent population.Every particle updates its position depending on the global best position(gbest)(for all details subband)and local best position(pbest)(for a subband).The fitness value is developed to terminate PSO when the difference between two local best(pbest)successors is smaller than a prescribe value.The experiments are applied on five different medical image types,i.e.,MRI,CT,and X-ray.Results show that the proposed algorithm can be more preferably to compress medical images than other existing wavelets techniques from peak signal to noise ratio(PSNR)and compression ratio(CR)points of views.
基金the Science Research Foundation of Education Department of ShaanxiProvince (08JK340)the Items of Xi’an University of Architecture and Technology(RC0701JC0718)
文摘The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.
文摘In this paper, wavelet transform and entropy are evaluated using the mathematical analysis concepts of reflexibility, regularity and series obtention, these concepts remark the reason to make a selective reference framework for power quality applications. With this idea the paper used the same treatment for the two algorithms (Multiresolution and Multiscale Entropy). The wavelet is denoted to have the most power full consistence to the light off the reflexibility, regularity and series obtention. The paper proposes a power quality technique namely MpqAT.
基金supported by the Geosciences and Technology Academy of China University of Petroleum(East China)
文摘Air-gun arrays are used in marine-seismic exploration. Far-field wavelets in subsurface media represent the stacking of single air-gun ideal wavelets. We derived single air-gun ideal wavelets using near-field wavelets recorded from near-field geophones and then synthesized them into far-field wavelets. This is critical for processing wavelets in marine- seismic exploration. For this purpose, several algorithms are currently used to decompose and synthesize wavelets in the time domain. If the traveltime of single air-gun wavelets is not an integral multiple of the sampling interval, the complex and error-prone resampling of the seismic signals using the time-domain method is necessary. Based on the relation between the frequency-domain phase and the time-domain time delay, we propose a method that first transforms the real near-field wavelet to the frequency domain via Fourier transforms; then, it decomposes it and composes the wavelet spectrum in the frequency domain, and then back transforms it to the time domain. Thus, the resampling problem is avoided and single air-gun wavelets and far-field wavelets can be reliably derived. The effect of ghost reflections is also considered, while decomposing the wavelet and removing the ghost reflections. Modeling and real data processing were used to demonstrate the feasibility of the proposed method.
文摘A novel multiresolution approach to the discrimination of textures using wavelets is presented. The approach employs an overcomplete wavelet decomposition called wavelet frames, which gives the description of both translation invariance and stability. In order to adapt to the quasi periodic property of textures, we propose the application of tree structured wavelet packet analysis. For discriminating efficiency, we develop a progressive texture discriminating algorithm, in which the discrimination process terminates once a suitably chosen discrimination criterion is met. Experiments show that with a minimal number of wavelet frame decompositions and iterations, our proposed approach could achieve a 100% correct discrimination rate on all the 12 texture types tested. That outperforms many of the existing approaches in terms of accuracy and computational efficiency, and thus it appears to be attractive for real time application involving texture based video/image classification.
