The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means ...The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means of the projection-slice theorem. The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.展开更多
Accurate estimation of fracture density and orientation is of great significance for seismic characterization of fractured reservoirs.Here,we propose a novel methodology to estimate fracture density and orientation fr...Accurate estimation of fracture density and orientation is of great significance for seismic characterization of fractured reservoirs.Here,we propose a novel methodology to estimate fracture density and orientation from azimuthal elastic impedance(AEI)difference using singular value decomposition(SVD).Based on Hudson's model,we first derive the AEI equation containing fracture density in HTI media,and then obtain basis functions and singular values from the normalized AEI difference utilizing SVD.Analysis shows that the basis function changing with azimuth is related to fracture orientation,fracture density is the linearly weighted sum of singular values,and the first singular value contributes the most to fracture density.Thus,we develop an SVD-based fracture density and orientation inversion approach constrained by smooth prior elastic parameters.Synthetic example shows that fracture density and orientation can be stably estimated,and the correlation coefficient between the true value and the estimated fracture density is above 0.85 even when an S/N ratio of 2.Field data example shows that the estimated fracture orientation is consistent with the interpretation of image log data,and the estimated fracture density reliably indicates fractured gas-bearing reservoir,which could help to guide the exploration and development of fractured reservoirs.展开更多
Source-generated noise, such as air, refracted, guided waves, near-surface multiples, and radial ground roll, is one of the most challenging problems in the land seismic method. The interference of the noise with refl...Source-generated noise, such as air, refracted, guided waves, near-surface multiples, and radial ground roll, is one of the most challenging problems in the land seismic method. The interference of the noise with reflection events often results in a distorted representation of the subsurface and gives rise to interpretation uncertainties. To suppress the noise, geophysicists have devised various techniques in both acquisition and processing stages. Conventional processing methods, such as high-pass, f - k and hyperbolic velocity filters, however, have certain disadvantages when handling actual seismic data. In this study, we present a new hybrid method combining singular value decomposition (SVD) with a special linear transformation of the common-shot gather. The method is aimed at effectively removing the noise while minimizing harm to the signal. As compared with other methods, the SVD-based one gives a denser approximation to source-generated noise before its subtraction from the seismic data, due to the use of more appropriate basis functions. The special transformation applied in advance to the data is intended to align the source-generated noise events horizontally and thus to benefit the subsequent SVD. The effectiveness of the method in suppressing source-generated noise is demonstrated with a synthetic data set. Emphasis is put on the comparison of the performance of the method with that of conventional f - k filtering.展开更多
Traditional watermark embedding schemes inevitably modify the data in a host audio signal and lead to the degradation of the host signal.In this paper,a novel audio zero-watermarking algorithm based on discrete wavele...Traditional watermark embedding schemes inevitably modify the data in a host audio signal and lead to the degradation of the host signal.In this paper,a novel audio zero-watermarking algorithm based on discrete wavelet transform(DWT),discrete cosine transform(DCT),and singular value decomposition(SVD) is presented.The watermark is registered by performing SVD on the coefficients generated through DWT and DCT to avoid data modification and host signal degradation.Simulation results show that the proposed zero-watermarking algorithm is strongly robust to common signal processing methods such as requantization,MP3 compression,resampling,addition of white Gaussian noise,and low-pass filtering.展开更多
In this paper,the singular value decomposition（SVD） method as a filter is applied before the tomographic inversion of soft-X-ray emission.Series of ＇filtered＇ signals including specific chronos and topos are obtai...In this paper,the singular value decomposition（SVD） method as a filter is applied before the tomographic inversion of soft-X-ray emission.Series of ＇filtered＇ signals including specific chronos and topos are obtained.（Here,chronos and topos are the decomposed spatial vectors and the decomposed temporal vectors,respectively）.Given specific magnetic flux function with coupling m = 1 and m = 2 modes,the line-integrated soft-X-ray signals at all chords have been obtained.Then m = 1 and m = 2 modes have been identified by tomography of simulated ＇filtered＇ signals extracted by the SVD method.Finaly,using the experimental line-integrated soft-X-ray signals,m = 2 competent mode of complex magnetohydrodynamics（MHD） activities during internal soft disruption is observed.This result demonstrates that m = 2 mode plays an important role in internal disruption（Here,m is the poloidal mode number）.展开更多
In this paper, we have developed an algorithm based on singular value decomposition （SVD） for matrix. And the novel SVD algorithm with normalized period of cardiac cycles is presented. The results from real magnetoc...In this paper, we have developed an algorithm based on singular value decomposition （SVD） for matrix. And the novel SVD algorithm with normalized period of cardiac cycles is presented. The results from real magnetocardiography （MCG） data processing show that the new algorithm is better than the standard one not only in suppressing noises, but also in providing high-fidelity MCG signals.展开更多
A variety of strong MHD instabilities are always resulted from MHD activity of Tokamak plasmas. Central MHD instabilities can be observed with pinhole cameras to record soft x-ray (SXR) emission from the plasma along ...A variety of strong MHD instabilities are always resulted from MHD activity of Tokamak plasmas. Central MHD instabilities can be observed with pinhole cameras to record soft x-ray (SXR) emission from the plasma along many chords with a high temporal resolution. The investigation of MHD instabilities often necessitates an analysis on spatial-temporal signals. The method of Singular Value Decomposition (SVD) can split such signals into orthogonal spatial and temporal vectors. By this means, the repetition time and the characteristic radius of various MHD phenomena such as sawteeth and snake-like perturbation can be obtained. Moreover, the (1,1) MHD mode is analyzed in great detail by SVD and used to determine the radius of the q = 1 surface.展开更多
In this paper,the singular value decomposition(SVD) method as a filter is applied before the tomographic inversion of soft-X-ray emission.Series of ’filtered’ signals including specific chronos and topos are obtaine...In this paper,the singular value decomposition(SVD) method as a filter is applied before the tomographic inversion of soft-X-ray emission.Series of ’filtered’ signals including specific chronos and topos are obtained.(Here,chronos and topos are the decomposed spatial vectors and the decomposed temporal vectors,respectively).Given specific magnetic flux function with coupling m = 1 and m = 2 modes,the line-integrated soft-X-ray signals at all chords have been obtained.Then m = 1 and m = 2 modes have been identified by tomography of simulated ’filtered’ signals extracted by the SVD method.Finaly,using the experimental line-integrated soft-X-ray signals,m = 2 competent mode of complex magnetohydrodynamics(MHD) activities during internal soft disruption is observed.This result demonstrates that m = 2 mode plays an important role in internal disruption(Here,m is the poloidal mode number).展开更多
针对工况传递路径分析(operational transfer path analysis,OTPA)测得振动信号存在大量高频噪声的问题,提出一种基于变分模态分解(variational mode decomposition,VMD)和奇异值分解(singular value decomposition,SVD)的组合降噪方法V...针对工况传递路径分析(operational transfer path analysis,OTPA)测得振动信号存在大量高频噪声的问题,提出一种基于变分模态分解(variational mode decomposition,VMD)和奇异值分解(singular value decomposition,SVD)的组合降噪方法VMD-SVD。该方法通过VMD算法对原始含噪信号进行分解,得到K个本征模态分量(intrinsic mode function,IMF);再通过方差贡献率(VCR)滤除含噪信号较大的IMF分量,并保留有效成分较多的IMF分量,经SVD算法对保留的IMF分量进行降噪处理;最后将降噪处理后的信号进行重构,得到本文组合降噪处理后的信号。本文通过模拟仿真实验验证上述方法的降噪效果,并将该方法运用到OTPA采集振动信号中。与其他基本降噪方法进行对比的结果表明,该方法能够有效滤除采集振动信号中的高频噪声,提高了OTPA方法的准确度以及信号后续分析处理的可靠性。展开更多
文摘The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means of the projection-slice theorem. The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.
基金sponsorship of the National Natural Science Foundation of China(41674130,U19B2008)the Postgraduate Innovation Project in China University of Petroleum(East China)(YCX2021016)for their funding this research。
文摘Accurate estimation of fracture density and orientation is of great significance for seismic characterization of fractured reservoirs.Here,we propose a novel methodology to estimate fracture density and orientation from azimuthal elastic impedance(AEI)difference using singular value decomposition(SVD).Based on Hudson's model,we first derive the AEI equation containing fracture density in HTI media,and then obtain basis functions and singular values from the normalized AEI difference utilizing SVD.Analysis shows that the basis function changing with azimuth is related to fracture orientation,fracture density is the linearly weighted sum of singular values,and the first singular value contributes the most to fracture density.Thus,we develop an SVD-based fracture density and orientation inversion approach constrained by smooth prior elastic parameters.Synthetic example shows that fracture density and orientation can be stably estimated,and the correlation coefficient between the true value and the estimated fracture density is above 0.85 even when an S/N ratio of 2.Field data example shows that the estimated fracture orientation is consistent with the interpretation of image log data,and the estimated fracture density reliably indicates fractured gas-bearing reservoir,which could help to guide the exploration and development of fractured reservoirs.
文摘Source-generated noise, such as air, refracted, guided waves, near-surface multiples, and radial ground roll, is one of the most challenging problems in the land seismic method. The interference of the noise with reflection events often results in a distorted representation of the subsurface and gives rise to interpretation uncertainties. To suppress the noise, geophysicists have devised various techniques in both acquisition and processing stages. Conventional processing methods, such as high-pass, f - k and hyperbolic velocity filters, however, have certain disadvantages when handling actual seismic data. In this study, we present a new hybrid method combining singular value decomposition (SVD) with a special linear transformation of the common-shot gather. The method is aimed at effectively removing the noise while minimizing harm to the signal. As compared with other methods, the SVD-based one gives a denser approximation to source-generated noise before its subtraction from the seismic data, due to the use of more appropriate basis functions. The special transformation applied in advance to the data is intended to align the source-generated noise events horizontally and thus to benefit the subsequent SVD. The effectiveness of the method in suppressing source-generated noise is demonstrated with a synthetic data set. Emphasis is put on the comparison of the performance of the method with that of conventional f - k filtering.
基金supported by the Open Foundation of Jiangsu Engineering Center of Network Monitoring(Nanjing University of Information Science&Technology)(Grant No.KJR1509)the PAPD fundthe CICAEET fund
文摘Traditional watermark embedding schemes inevitably modify the data in a host audio signal and lead to the degradation of the host signal.In this paper,a novel audio zero-watermarking algorithm based on discrete wavelet transform(DWT),discrete cosine transform(DCT),and singular value decomposition(SVD) is presented.The watermark is registered by performing SVD on the coefficients generated through DWT and DCT to avoid data modification and host signal degradation.Simulation results show that the proposed zero-watermarking algorithm is strongly robust to common signal processing methods such as requantization,MP3 compression,resampling,addition of white Gaussian noise,and low-pass filtering.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10935004)
文摘In this paper,the singular value decomposition（SVD） method as a filter is applied before the tomographic inversion of soft-X-ray emission.Series of ＇filtered＇ signals including specific chronos and topos are obtained.（Here,chronos and topos are the decomposed spatial vectors and the decomposed temporal vectors,respectively）.Given specific magnetic flux function with coupling m = 1 and m = 2 modes,the line-integrated soft-X-ray signals at all chords have been obtained.Then m = 1 and m = 2 modes have been identified by tomography of simulated ＇filtered＇ signals extracted by the SVD method.Finaly,using the experimental line-integrated soft-X-ray signals,m = 2 competent mode of complex magnetohydrodynamics（MHD） activities during internal soft disruption is observed.This result demonstrates that m = 2 mode plays an important role in internal disruption（Here,m is the poloidal mode number）.
文摘In this paper, we have developed an algorithm based on singular value decomposition （SVD） for matrix. And the novel SVD algorithm with normalized period of cardiac cycles is presented. The results from real magnetocardiography （MCG） data processing show that the new algorithm is better than the standard one not only in suppressing noises, but also in providing high-fidelity MCG signals.
基金The project supported by the National Nature Science Foundation of China (No. 10075014) and the Tenth-Five-Year Nuclear Energy Development of the Commission of Science Technology and Industry for National Defense, and of the China National Nuclear Corpor
文摘A variety of strong MHD instabilities are always resulted from MHD activity of Tokamak plasmas. Central MHD instabilities can be observed with pinhole cameras to record soft x-ray (SXR) emission from the plasma along many chords with a high temporal resolution. The investigation of MHD instabilities often necessitates an analysis on spatial-temporal signals. The method of Singular Value Decomposition (SVD) can split such signals into orthogonal spatial and temporal vectors. By this means, the repetition time and the characteristic radius of various MHD phenomena such as sawteeth and snake-like perturbation can be obtained. Moreover, the (1,1) MHD mode is analyzed in great detail by SVD and used to determine the radius of the q = 1 surface.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10935004)
文摘In this paper,the singular value decomposition(SVD) method as a filter is applied before the tomographic inversion of soft-X-ray emission.Series of ’filtered’ signals including specific chronos and topos are obtained.(Here,chronos and topos are the decomposed spatial vectors and the decomposed temporal vectors,respectively).Given specific magnetic flux function with coupling m = 1 and m = 2 modes,the line-integrated soft-X-ray signals at all chords have been obtained.Then m = 1 and m = 2 modes have been identified by tomography of simulated ’filtered’ signals extracted by the SVD method.Finaly,using the experimental line-integrated soft-X-ray signals,m = 2 competent mode of complex magnetohydrodynamics(MHD) activities during internal soft disruption is observed.This result demonstrates that m = 2 mode plays an important role in internal disruption(Here,m is the poloidal mode number).
文摘针对工况传递路径分析(operational transfer path analysis,OTPA)测得振动信号存在大量高频噪声的问题,提出一种基于变分模态分解(variational mode decomposition,VMD)和奇异值分解(singular value decomposition,SVD)的组合降噪方法VMD-SVD。该方法通过VMD算法对原始含噪信号进行分解,得到K个本征模态分量(intrinsic mode function,IMF);再通过方差贡献率(VCR)滤除含噪信号较大的IMF分量,并保留有效成分较多的IMF分量,经SVD算法对保留的IMF分量进行降噪处理;最后将降噪处理后的信号进行重构,得到本文组合降噪处理后的信号。本文通过模拟仿真实验验证上述方法的降噪效果,并将该方法运用到OTPA采集振动信号中。与其他基本降噪方法进行对比的结果表明,该方法能够有效滤除采集振动信号中的高频噪声,提高了OTPA方法的准确度以及信号后续分析处理的可靠性。
