A point spread function（PSF） for the blurring component in positron emission tomography（PET） is studied. The PSF matrix is derived from the single photon incidence response function. A statistical iterative recons...A point spread function（PSF） for the blurring component in positron emission tomography（PET） is studied. The PSF matrix is derived from the single photon incidence response function. A statistical iterative reconstruction（IR） method based on the system matrix containing the PSF is developed. More specifically, the gamma photon incidence upon a crystal array is simulated by Monte Carlo（MC） simulation, and then the single photon incidence response functions are calculated. Subsequently, the single photon incidence response functions are used to compute the coincidence blurring factor according to the physical process of PET coincidence detection. Through weighting the ordinary system matrix response by the coincidence blurring factors, the IR system matrix containing the PSF is finally established. By using this system matrix, the image is reconstructed by an ordered subset expectation maximization（OSEM） algorithm. The experimental results show that the proposed system matrix can substantially improve the image radial resolution, contrast,and noise property. Furthermore, the simulated single gamma-ray incidence response function depends only on the crystal configuration, so the method could be extended to any PET scanner with the same detector crystal configuration.展开更多
Through the analysis of roundness error separation technique of three-point method and based on the invariability and periodicity of the geometrical characteristic of measured round contour, a new matrix algorithm, wh...Through the analysis of roundness error separation technique of three-point method and based on the invariability and periodicity of the geometrical characteristic of measured round contour, a new matrix algorithm, which can be used to solve directly the roundness of the measured round contour without Fourier transform, is presented. On the basis of the research and analysis of the rotation error movement which is separated by using the three-point method, a mathematical equation is derived, which can be used to separate the eccentric motion of least square center of measured round contour and the pure rotation motion error of spindle in rotation motion. The correctness of this method is validated by means of simulation.展开更多
A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more strin...A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more stringent than the optimal bounds by Wolkowicz and Styan in specific cases.展开更多
Transverse opening in a beam has a reducing effect of the beam stiffness which will cause a significant increase in beam deflection in the region on the opening. In this paper, a new stiffness matrix for a beam elemen...Transverse opening in a beam has a reducing effect of the beam stiffness which will cause a significant increase in beam deflection in the region on the opening. In this paper, a new stiffness matrix for a beam element with transverse opening including the effect of shear deformation has been derived. The strain energy principle is used in the derivation process of the stiffness matrix and the fixed-end force vector for the case of a concentrated or a uniformly distributed load is also derived. The accuracy of the obtained results based on the derived stiffness matrix is examined through comparison with that of the finite element method using Abaqus package and a previous study which show a good agreement with high accuracy.展开更多
Hierarchical mobile IPv6 （HMIPv6） introduces a mobility anchor point to reduce the signaling overhead and handoff latency. In this paper, we apply the matrix-analytical approach to explore the performance measures o...Hierarchical mobile IPv6 （HMIPv6） introduces a mobility anchor point to reduce the signaling overhead and handoff latency. In this paper, we apply the matrix-analytical approach to explore the performance measures of the ongoing mobile nodes （MNs） drop and new MNs block probabilities of mobility anchor point with a guard bandwidth reservation scheme. We apply the Markovian arrival process （MAP） to model ongoing MNs and new MNs. Five related performance measures are derived, including the long-term new MN block and ongoing MN drop probabilities, and the three short-term measures of average length of a block period and a non-block period, as well as the conditional ongoing MN drop probability during a block period. These performance measures greatly assist the guard bandwidth reservation mechanism in determining a proper threshold guard bandwidth. The results presented in this paper can provide guidelines for designing adaptive algorithms to adjust the threshold in the guard bandwidth reservation scheme.展开更多
In this paper, we obtain a formula for the derivative of a determinant with respect to an eigenvalue in the modified Cholesky decomposition of a symmetric matrix, a characteristic example of a direct solution method i...In this paper, we obtain a formula for the derivative of a determinant with respect to an eigenvalue in the modified Cholesky decomposition of a symmetric matrix, a characteristic example of a direct solution method in computational linear algebra. We apply our proposed formula to a technique used in nonlinear finite-element methods and discuss methods for determining singular points, such as bifurcation points and limit points. In our proposed method, the increment in arc length (or other relevant quantities) may be determined automatically, allowing a reduction in the number of basic parameters. The method is particularly effective for banded matrices, which allow a significant reduction in memory requirements as compared to dense matrices. We discuss the theoretical foundations of our proposed method, present algorithms and programs that implement it, and conduct numerical experiments to investigate its effectiveness.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.Y4811H805C and 81101175)
文摘A point spread function（PSF） for the blurring component in positron emission tomography（PET） is studied. The PSF matrix is derived from the single photon incidence response function. A statistical iterative reconstruction（IR） method based on the system matrix containing the PSF is developed. More specifically, the gamma photon incidence upon a crystal array is simulated by Monte Carlo（MC） simulation, and then the single photon incidence response functions are calculated. Subsequently, the single photon incidence response functions are used to compute the coincidence blurring factor according to the physical process of PET coincidence detection. Through weighting the ordinary system matrix response by the coincidence blurring factors, the IR system matrix containing the PSF is finally established. By using this system matrix, the image is reconstructed by an ordered subset expectation maximization（OSEM） algorithm. The experimental results show that the proposed system matrix can substantially improve the image radial resolution, contrast,and noise property. Furthermore, the simulated single gamma-ray incidence response function depends only on the crystal configuration, so the method could be extended to any PET scanner with the same detector crystal configuration.
基金Henan Innovation Project for University Prominent Research Talents (2004KYCX006)Ph.D.Inital Foundation of Henan University of Science &Techonologythe Natural Science Foundation of Henan Education Agency (2008A460007)
文摘Through the analysis of roundness error separation technique of three-point method and based on the invariability and periodicity of the geometrical characteristic of measured round contour, a new matrix algorithm, which can be used to solve directly the roundness of the measured round contour without Fourier transform, is presented. On the basis of the research and analysis of the rotation error movement which is separated by using the three-point method, a mathematical equation is derived, which can be used to separate the eccentric motion of least square center of measured round contour and the pure rotation motion error of spindle in rotation motion. The correctness of this method is validated by means of simulation.
文摘A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more stringent than the optimal bounds by Wolkowicz and Styan in specific cases.
文摘Transverse opening in a beam has a reducing effect of the beam stiffness which will cause a significant increase in beam deflection in the region on the opening. In this paper, a new stiffness matrix for a beam element with transverse opening including the effect of shear deformation has been derived. The strain energy principle is used in the derivation process of the stiffness matrix and the fixed-end force vector for the case of a concentrated or a uniformly distributed load is also derived. The accuracy of the obtained results based on the derived stiffness matrix is examined through comparison with that of the finite element method using Abaqus package and a previous study which show a good agreement with high accuracy.
文摘Hierarchical mobile IPv6 （HMIPv6） introduces a mobility anchor point to reduce the signaling overhead and handoff latency. In this paper, we apply the matrix-analytical approach to explore the performance measures of the ongoing mobile nodes （MNs） drop and new MNs block probabilities of mobility anchor point with a guard bandwidth reservation scheme. We apply the Markovian arrival process （MAP） to model ongoing MNs and new MNs. Five related performance measures are derived, including the long-term new MN block and ongoing MN drop probabilities, and the three short-term measures of average length of a block period and a non-block period, as well as the conditional ongoing MN drop probability during a block period. These performance measures greatly assist the guard bandwidth reservation mechanism in determining a proper threshold guard bandwidth. The results presented in this paper can provide guidelines for designing adaptive algorithms to adjust the threshold in the guard bandwidth reservation scheme.
文摘In this paper, we obtain a formula for the derivative of a determinant with respect to an eigenvalue in the modified Cholesky decomposition of a symmetric matrix, a characteristic example of a direct solution method in computational linear algebra. We apply our proposed formula to a technique used in nonlinear finite-element methods and discuss methods for determining singular points, such as bifurcation points and limit points. In our proposed method, the increment in arc length (or other relevant quantities) may be determined automatically, allowing a reduction in the number of basic parameters. The method is particularly effective for banded matrices, which allow a significant reduction in memory requirements as compared to dense matrices. We discuss the theoretical foundations of our proposed method, present algorithms and programs that implement it, and conduct numerical experiments to investigate its effectiveness.
