An orthogonal wavelet transform fractionally spaced blind equalization algorithm based on the optimization of genetic algorithm(WTFSE-GA) is proposed in viewof the lowconvergence rate,large steady-state mean square er...An orthogonal wavelet transform fractionally spaced blind equalization algorithm based on the optimization of genetic algorithm(WTFSE-GA) is proposed in viewof the lowconvergence rate,large steady-state mean square error and local convergence of traditional constant modulus blind equalization algorithm(CMA).The proposed algorithm can reduce the signal autocorrelation through the orthogonal wavelet transform of input signal of fractionally spaced blind equalizer,and decrease the possibility of CMA local convergence by using the global random search characteristics of genetic algorithm to optimize the equalizer weight vector.The proposed algorithm has the faster convergence rate and smaller mean square error compared with FSE and WT-FSE.The efficiency of the proposed algorithm is proved by computer simulation of underwater acoustic channels.展开更多
Efficiency of the autofocusing algorithm implementations based on various orthogonal transforms is examined. The algorithm uses the variance of an image acquired by a sensor as a focus function. To compute the estimat...Efficiency of the autofocusing algorithm implementations based on various orthogonal transforms is examined. The algorithm uses the variance of an image acquired by a sensor as a focus function. To compute the estimate of the variance we exploit the equivalence between that estimate and the image orthogonal expansion. Energy consumption of three implementations exploiting either of the following fast orthogonal transforms: the discrete cosine, the Walsh-Hadamard, and the Haar wavelet one, is evaluated and compared. Furthermore, it is conjectured that the computation precision can considerably be reduced if the image is heavily corrupted by the noise, and a simple problem of optimal word bit-length selection with respect to the signal variance is analyzed.展开更多
In recent years,it has been evident that internet is the most effective means of transmitting information in the form of documents,photographs,or videos around the world.The purpose of an image compression method is t...In recent years,it has been evident that internet is the most effective means of transmitting information in the form of documents,photographs,or videos around the world.The purpose of an image compression method is to encode a picture with fewer bits while retaining the decompressed image’s visual quality.During transmission,this massive data necessitates a lot of channel space.In order to overcome this problem,an effective visual compression approach is required to resize this large amount of data.This work is based on lossy image compression and is offered for static color images.The quantization procedure determines the compressed data quality characteristics.The images are converted from RGB to International Commission on Illumination CIE La^(∗)b^(∗);and YCbCr color spaces before being used.In the transform domain,the color planes are encoded using the proposed quantization matrix.To improve the efficiency and quality of the compressed image,the standard quantization matrix is updated with the respective image block.We used seven discrete orthogonal transforms,including five variations of the Complex Hadamard Transform,Discrete Fourier Transform and Discrete Cosine Transform,as well as thresholding,quantization,de-quantization and inverse discrete orthogonal transforms with CIE La^(∗)b^(∗);and YCbCr to RGB conversion.Peak to signal noise ratio,signal to noise ratio,picture similarity index and compression ratio are all used to assess the quality of compressed images.With the relevant transforms,the image size and bits per pixel are also explored.Using the(n,n)block of transform,adaptive scanning is used to acquire the best feasible compression ratio.Because of these characteristics,multimedia systems and services have a wide range of possible applications.展开更多
ions in the ECG signal.The cardiologist and medical specialistfind numerous difficulties in the process of traditional approaches.The specified restrictions are eliminated in the proposed classifier.The fundamental ai...ions in the ECG signal.The cardiologist and medical specialistfind numerous difficulties in the process of traditional approaches.The specified restrictions are eliminated in the proposed classifier.The fundamental aim of this work is tofind the R-R interval.To analyze the blockage,different approaches are implemented,which make the computation as facile with high accuracy.The information are recovered from the MIT-BIH dataset.The retrieved data contain normal and pathological ECG signals.To obtain a noiseless signal,Gaborfilter is employed and to compute the amplitude of the signal,DCT-DOST(Discrete cosine based Discrete orthogonal stock well transform)is implemented.The amplitude is computed to detect the cardiac abnormality.The R peak of the underlying ECG signal is noted and the segment length of the ECG cycle is identified.The Genetic algorithm(GA)retrieves the primary highlights and the classifier integrates the data with the chosen attributes to optimize the identification.In addition,the GA helps in performing hereditary calculations to reduce the problem of multi-target enhancement.Finally,the RBFNN(Radial basis function neural network)is applied,which diminishes the local minima present in the signal.It shows enhancement in characterizing the ordinary and anomalous ECG signals.展开更多
The Gauss-Markov (GM) model and the Errors-in-Variables (EIV) model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation e...The Gauss-Markov (GM) model and the Errors-in-Variables (EIV) model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation errors in original coordinates system are also taken into account, the latter is more accurate and reasonable than the former. Although the Weighted Total Least Squares (WTLS) technique has been intro- duced into coordinate transformations as the measured points are heteroscedastic and correlated, the Variance- Covariance Matrix (VCM) of observations is restricted by a particular structure, namely, only the correlations of each points are taken into account. Because the 3D datum transformation with large rotation angle is a non- linear problem, the WTLS is no longer suitable in this ease. In this contribution, we suggested the nonlinear WTLS adjustments with equality constraints (NWTLS-EC) for 3D datum transformation with large rotation an- gle, which removed the particular structure restriction on the VCM. The Least Squares adjustment with Equality (LSE) constraints is employed to solve NWTLS-EC as the nonlinear model has been linearized, and an iterative algorithm is proposed with the LSE solution. A simulation study of 3D datum transformation with large rotation angle is given to insight into the feasibility of our algorithm at last.展开更多
As one of the typical less-mobility parallel mechanisms,the spherical parallel mechanism U_(P + R) with two degrees of freedom(2-DOF)possess high order overconstraints,and the calculation of its stiffness is partly di...As one of the typical less-mobility parallel mechanisms,the spherical parallel mechanism U_(P + R) with two degrees of freedom(2-DOF)possess high order overconstraints,and the calculation of its stiffness is partly different with general parallel mechanisms owing to the bars in each branch are assumed to be arc-shaped.By means of small deformation superposition principle,the relationship between the angle displacement and line displacement of moving platform and the forces acted on the branches were derived out.Based on the results of static analysis,the relationship between the applied force,the line displacement and the angle displacement of the mechanism was set up.And then the stiffness matrix was obtained.The six principal stiffness of the mechanism and the corresponding directions were achieved by the orthogonal transformation.The numerical calculation was performed and the results showed that the principal stiffness and directions are varied with the pose-position of the mechanism,and the principal stiffness is gradually enlarged when it is far away from the origin.In addition,the torsion stiffness is much greater and the line deformation stiffness is smaller,the difference between the two parts is huge.The research content of this paper supplies the theoretical foundation for the further engineering design and application of the spherical parallel mechanism.展开更多
In an inner-product space, an invertible vector generates a reflection with respect to a hyperplane, and the Clifford product of several invertible vectors, called a versor in Clifford algebra, generates the compositi...In an inner-product space, an invertible vector generates a reflection with respect to a hyperplane, and the Clifford product of several invertible vectors, called a versor in Clifford algebra, generates the composition of the corresponding reflections, which is an orthogonal transformation. Given a versor in a Clifford algebra, finding another sequence of invertible vectors of strictly shorter length but whose Clifford product still equals the input versor, is called versor compression. Geometrically, versor compression is equivalent to decomposing an orthogonal transformation into a shorter sequence of reflections. This paper proposes a simple algorithm of compressing versors of symbolic form in Clifford algebra. The algorithm is based on computing the intersections of lines with planes in the corresponding Grassmann-Cayley algebra, and is complete in the case of Euclidean or Minkowski inner-product space.展开更多
Dependence among random input variables affects importantly the results of probabilistic load flow(PLF),system economic operation,and system security.To solve this problem,the main objectiveness of the paper is to ana...Dependence among random input variables affects importantly the results of probabilistic load flow(PLF),system economic operation,and system security.To solve this problem,the main objectiveness of the paper is to analyze the performance of several schemes for simulating correlated variables combined with the point estimate method(PEM).Unlike the existing works that considering one single scheme combined with Monte Carlo simulation(MCS) or PEM,by neglecting the correlation among random input variables,four schemes were presented for disposing the dependence of correlated random variables,including Nataf transformation /polynomial normal transformation(PINT) combined with orthogonal transformation(OT) / elementary transformation(ET).Combining with the 2m+1 approach of PEM,a space transformation-based formulation was proposed and adopted for solving the PLF.The proposed approach is applied in the modified IEEE 30-bus system while considering correlated wind generations and load demands.Numerical results show the effectiveness of the proposed approach compared with those obtained from the MCS.Results also show that the scheme of combining Nataf transformation and ET with PEM provides the best performance.展开更多
Efficient representation of linear singularities is discussed in this paper. We analyzed the relationship between the "wrap around" effect and the distribution of FRAT (Finite Radon Transform) coefficients first, ...Efficient representation of linear singularities is discussed in this paper. We analyzed the relationship between the "wrap around" effect and the distribution of FRAT (Finite Radon Transform) coefficients first, and then based on study of some properties of the columnwisely FRAT reconstruction procedure, we proposed an energy-based adaptive orthogonal FRIT scheme (EFRIT). Experiments using nonlinear approximation show its superiority in energy concentration over both Discrete Wavelet Transform (DWT) and Finite Ridgelet Transform (FRIT). Furthermore, we have modeled the denoising problem and proposed a novel threshold selecting method. Experiments carried out on images containing strong linear singularities and texture components with varying levels of addictive white Gaussian noise show that our method achieves prominent improvement in terms of both SNR and visual quality as compared with that of DWT and FRIT.展开更多
Flattening of the interfaces is necessary in computing wave propagation along strati?ed waveguides in large range step sizes while using marching methods. When the supposition that there exists one horizontal straight...Flattening of the interfaces is necessary in computing wave propagation along strati?ed waveguides in large range step sizes while using marching methods. When the supposition that there exists one horizontal straight line in two adjacent interfaces does not hold, the previously suggested local orthogonal transform method with an analytical formulation is not feasible. This paper presents a numerical coordinate transform and an equation transform to perform the transforms numerically for waveguides without satisfying the supposition. The boundary value problem is then reduced to an initial value problem by one-way reformulation based on the Dirichlet-to-Neumann (DtN) map. This method is applicable in solving long-range wave propagation problems in slowly varying waveguides with a multilayered medium structure.展开更多
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations.In particular,a knowledge of the symmetries may help decrease the...Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations.In particular,a knowledge of the symmetries may help decrease the problem dimension,reduce the size of the search space by means of linear cuts.While the previous studies of symmetries in the mathematical programming usually dealt with permutations of coordinates of the solutions space,the present paper considers a larger group of invertible linear transformations.We study a special case of the quadratic programming problem,where the objective function and constraints are given by quadratic forms.We formulate conditions,which allow us to transform the original problem to a new system of coordinates,such that the symmetries may be sought only among orthogonal transformations.In particular,these conditions are satisfied if the sum of all matrices of quadratic forms,involved in the constraints,is a positive definite matrix.We describe the structure and some useful properties of the group of symmetries of the problem.Besides that,the methods of detection of such symmetries are outlined for different special cases as well as for the general case.展开更多
We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second mom...We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets. We use orthogonai transformations to overcome the difficulty produced by those singular matrixes, and the analytical form of the efficient frontier is obtained. As an application, the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.展开更多
基金Sponsored by the Nature Science Foundation of Jiangsu(BK2009410)
文摘An orthogonal wavelet transform fractionally spaced blind equalization algorithm based on the optimization of genetic algorithm(WTFSE-GA) is proposed in viewof the lowconvergence rate,large steady-state mean square error and local convergence of traditional constant modulus blind equalization algorithm(CMA).The proposed algorithm can reduce the signal autocorrelation through the orthogonal wavelet transform of input signal of fractionally spaced blind equalizer,and decrease the possibility of CMA local convergence by using the global random search characteristics of genetic algorithm to optimize the equalizer weight vector.The proposed algorithm has the faster convergence rate and smaller mean square error compared with FSE and WT-FSE.The efficiency of the proposed algorithm is proved by computer simulation of underwater acoustic channels.
基金supported by the NCN grant UMO-2011/01/B/ST7/00666.
文摘Efficiency of the autofocusing algorithm implementations based on various orthogonal transforms is examined. The algorithm uses the variance of an image acquired by a sensor as a focus function. To compute the estimate of the variance we exploit the equivalence between that estimate and the image orthogonal expansion. Energy consumption of three implementations exploiting either of the following fast orthogonal transforms: the discrete cosine, the Walsh-Hadamard, and the Haar wavelet one, is evaluated and compared. Furthermore, it is conjectured that the computation precision can considerably be reduced if the image is heavily corrupted by the noise, and a simple problem of optimal word bit-length selection with respect to the signal variance is analyzed.
文摘In recent years,it has been evident that internet is the most effective means of transmitting information in the form of documents,photographs,or videos around the world.The purpose of an image compression method is to encode a picture with fewer bits while retaining the decompressed image’s visual quality.During transmission,this massive data necessitates a lot of channel space.In order to overcome this problem,an effective visual compression approach is required to resize this large amount of data.This work is based on lossy image compression and is offered for static color images.The quantization procedure determines the compressed data quality characteristics.The images are converted from RGB to International Commission on Illumination CIE La^(∗)b^(∗);and YCbCr color spaces before being used.In the transform domain,the color planes are encoded using the proposed quantization matrix.To improve the efficiency and quality of the compressed image,the standard quantization matrix is updated with the respective image block.We used seven discrete orthogonal transforms,including five variations of the Complex Hadamard Transform,Discrete Fourier Transform and Discrete Cosine Transform,as well as thresholding,quantization,de-quantization and inverse discrete orthogonal transforms with CIE La^(∗)b^(∗);and YCbCr to RGB conversion.Peak to signal noise ratio,signal to noise ratio,picture similarity index and compression ratio are all used to assess the quality of compressed images.With the relevant transforms,the image size and bits per pixel are also explored.Using the(n,n)block of transform,adaptive scanning is used to acquire the best feasible compression ratio.Because of these characteristics,multimedia systems and services have a wide range of possible applications.
文摘ions in the ECG signal.The cardiologist and medical specialistfind numerous difficulties in the process of traditional approaches.The specified restrictions are eliminated in the proposed classifier.The fundamental aim of this work is tofind the R-R interval.To analyze the blockage,different approaches are implemented,which make the computation as facile with high accuracy.The information are recovered from the MIT-BIH dataset.The retrieved data contain normal and pathological ECG signals.To obtain a noiseless signal,Gaborfilter is employed and to compute the amplitude of the signal,DCT-DOST(Discrete cosine based Discrete orthogonal stock well transform)is implemented.The amplitude is computed to detect the cardiac abnormality.The R peak of the underlying ECG signal is noted and the segment length of the ECG cycle is identified.The Genetic algorithm(GA)retrieves the primary highlights and the classifier integrates the data with the chosen attributes to optimize the identification.In addition,the GA helps in performing hereditary calculations to reduce the problem of multi-target enhancement.Finally,the RBFNN(Radial basis function neural network)is applied,which diminishes the local minima present in the signal.It shows enhancement in characterizing the ordinary and anomalous ECG signals.
基金supported by the National Natural Science Foundation of China(41074017)
文摘The Gauss-Markov (GM) model and the Errors-in-Variables (EIV) model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation errors in original coordinates system are also taken into account, the latter is more accurate and reasonable than the former. Although the Weighted Total Least Squares (WTLS) technique has been intro- duced into coordinate transformations as the measured points are heteroscedastic and correlated, the Variance- Covariance Matrix (VCM) of observations is restricted by a particular structure, namely, only the correlations of each points are taken into account. Because the 3D datum transformation with large rotation angle is a non- linear problem, the WTLS is no longer suitable in this ease. In this contribution, we suggested the nonlinear WTLS adjustments with equality constraints (NWTLS-EC) for 3D datum transformation with large rotation an- gle, which removed the particular structure restriction on the VCM. The Least Squares adjustment with Equality (LSE) constraints is employed to solve NWTLS-EC as the nonlinear model has been linearized, and an iterative algorithm is proposed with the LSE solution. A simulation study of 3D datum transformation with large rotation angle is given to insight into the feasibility of our algorithm at last.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51275443 and 51005195)Key Project of Chinese Ministry of Education(Grant No.212012)+1 种基金Research Fund for the Doctoral Program of Higher Education of China(Grant No.20111333120004)Natural Science Foundationof Hebei Province(Grant No.E2012203034)
文摘As one of the typical less-mobility parallel mechanisms,the spherical parallel mechanism U_(P + R) with two degrees of freedom(2-DOF)possess high order overconstraints,and the calculation of its stiffness is partly different with general parallel mechanisms owing to the bars in each branch are assumed to be arc-shaped.By means of small deformation superposition principle,the relationship between the angle displacement and line displacement of moving platform and the forces acted on the branches were derived out.Based on the results of static analysis,the relationship between the applied force,the line displacement and the angle displacement of the mechanism was set up.And then the stiffness matrix was obtained.The six principal stiffness of the mechanism and the corresponding directions were achieved by the orthogonal transformation.The numerical calculation was performed and the results showed that the principal stiffness and directions are varied with the pose-position of the mechanism,and the principal stiffness is gradually enlarged when it is far away from the origin.In addition,the torsion stiffness is much greater and the line deformation stiffness is smaller,the difference between the two parts is huge.The research content of this paper supplies the theoretical foundation for the further engineering design and application of the spherical parallel mechanism.
文摘In an inner-product space, an invertible vector generates a reflection with respect to a hyperplane, and the Clifford product of several invertible vectors, called a versor in Clifford algebra, generates the composition of the corresponding reflections, which is an orthogonal transformation. Given a versor in a Clifford algebra, finding another sequence of invertible vectors of strictly shorter length but whose Clifford product still equals the input versor, is called versor compression. Geometrically, versor compression is equivalent to decomposing an orthogonal transformation into a shorter sequence of reflections. This paper proposes a simple algorithm of compressing versors of symbolic form in Clifford algebra. The algorithm is based on computing the intersections of lines with planes in the corresponding Grassmann-Cayley algebra, and is complete in the case of Euclidean or Minkowski inner-product space.
基金National Science Foundation of China(No.61533010)the Science and Technology Commission of Shanghai Municipality,China(No.14ZR1415300)
文摘Dependence among random input variables affects importantly the results of probabilistic load flow(PLF),system economic operation,and system security.To solve this problem,the main objectiveness of the paper is to analyze the performance of several schemes for simulating correlated variables combined with the point estimate method(PEM).Unlike the existing works that considering one single scheme combined with Monte Carlo simulation(MCS) or PEM,by neglecting the correlation among random input variables,four schemes were presented for disposing the dependence of correlated random variables,including Nataf transformation /polynomial normal transformation(PINT) combined with orthogonal transformation(OT) / elementary transformation(ET).Combining with the 2m+1 approach of PEM,a space transformation-based formulation was proposed and adopted for solving the PLF.The proposed approach is applied in the modified IEEE 30-bus system while considering correlated wind generations and load demands.Numerical results show the effectiveness of the proposed approach compared with those obtained from the MCS.Results also show that the scheme of combining Nataf transformation and ET with PEM provides the best performance.
基金Scientific Research Foundation for the Returned Overseas Chinese Scholarsthe Ministry of Education (Grant No. 2004.176.4)the Natural Science Foundation of Shandong Province (Grant Nos. Z2004G01 and 2004ZRC03016)
文摘Efficient representation of linear singularities is discussed in this paper. We analyzed the relationship between the "wrap around" effect and the distribution of FRAT (Finite Radon Transform) coefficients first, and then based on study of some properties of the columnwisely FRAT reconstruction procedure, we proposed an energy-based adaptive orthogonal FRIT scheme (EFRIT). Experiments using nonlinear approximation show its superiority in energy concentration over both Discrete Wavelet Transform (DWT) and Finite Ridgelet Transform (FRIT). Furthermore, we have modeled the denoising problem and proposed a novel threshold selecting method. Experiments carried out on images containing strong linear singularities and texture components with varying levels of addictive white Gaussian noise show that our method achieves prominent improvement in terms of both SNR and visual quality as compared with that of DWT and FRIT.
基金Project supported by the Program for New Century Excel-lent Talents in University (No. NCET-08-0450)the 985 II of Xi’an Jiaotong University, and the High Talented Person Scientific Research Start Project of North China University of Water Resources and Electric Power (No. 003001)
文摘Flattening of the interfaces is necessary in computing wave propagation along strati?ed waveguides in large range step sizes while using marching methods. When the supposition that there exists one horizontal straight line in two adjacent interfaces does not hold, the previously suggested local orthogonal transform method with an analytical formulation is not feasible. This paper presents a numerical coordinate transform and an equation transform to perform the transforms numerically for waveguides without satisfying the supposition. The boundary value problem is then reduced to an initial value problem by one-way reformulation based on the Dirichlet-to-Neumann (DtN) map. This method is applicable in solving long-range wave propagation problems in slowly varying waveguides with a multilayered medium structure.
基金funded in accordance with the state task of the Omsk Scientific Center SB RAS(project registration No.122011200349-3).The work on Sections 1,4 and 9 was funded in accordance with the state task of the IM SB RAS(project FWNF-2022-0020).
文摘Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations.In particular,a knowledge of the symmetries may help decrease the problem dimension,reduce the size of the search space by means of linear cuts.While the previous studies of symmetries in the mathematical programming usually dealt with permutations of coordinates of the solutions space,the present paper considers a larger group of invertible linear transformations.We study a special case of the quadratic programming problem,where the objective function and constraints are given by quadratic forms.We formulate conditions,which allow us to transform the original problem to a new system of coordinates,such that the symmetries may be sought only among orthogonal transformations.In particular,these conditions are satisfied if the sum of all matrices of quadratic forms,involved in the constraints,is a positive definite matrix.We describe the structure and some useful properties of the group of symmetries of the problem.Besides that,the methods of detection of such symmetries are outlined for different special cases as well as for the general case.
基金National Basic Research Program of China (973 Program No.2007CB814903)National Natural Science Foundation of China (No.70671069)
文摘We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets. We use orthogonai transformations to overcome the difficulty produced by those singular matrixes, and the analytical form of the efficient frontier is obtained. As an application, the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10371008)a grant of Jingshi Scholar of Beijing Normal University.