PET image reconstruction with a system matrix containing point spread function derived from single photon incidence response

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.

Stability Analysis of DC Microgrid Clusters Based on Step-by-step System Matrix Building Algorithm

DC microgrids(DCMGs)are made up of a network of sources and loads that are connected by a number of power electronic converters(PECs).The increase in the number of these PECs instigates major concerns in system stability.While interconnecting the microgrids to form a cluster,the system stability must be ensured.This paper proposes a novel stepby-step system matrix building(SMB)algorithm to update the system matrix of an existing DCMG cluster when a new microgrid is added to the cluster through a distribution line.The stability of the individual DCMGs and the DCMG cluster is analyzed using the eigenvalue method.Further,the particle swarm optimization(PSO)algorithm is used to retune the controller gains if the newly formed cluster is not stable.The simulation of the DCMG cluster is carried out in MATLAB/Simulink environment to test the proposed algorithm.The results are also validated using the OP4510 real-time simulator(RTS).

Image reconstruction for the coded aperture system in nuclear safety and security using a Monte Carlo-based system matrix

Purpose Accurate localization of radioactive materials is critical to nuclear safety and nuclear security.A coded aperture imaging system provides a visualization solution.However,the correlation method has poor reconstruction performance for sources with low counts and for extended sources.Methods In this study,a Monte Carlo optimization-based MLEM algorithm(MC-MLEM)is proposed.The system matrix was obtained by accurate Monte Carlo simulation,so the physical effects such as mask penetration that affect the imaging process were taken into account in the MLEM algorithm.In the simulation process,the normalization of the system matrix was realized by controlling the source at different position of the source plane to have the same activity and emission angle.Results The experimental results showed that compared with the correlation method,the MC-MLEM algorithm could improve the signal-to-noise ratio and angular resolution and locate the source position quickly and accurately under low count conditions.Furthermore,the MC-MLEM algorithm could reconstruct the shape of the extended source and the expected activity ratio of cold-hot sources with large activity differences.Conclusion The MC-MLEM algorithm improved the imaging results and enhanced the reconstruction performance.

Fast and accurate generation method of PSF-based system matrix for PET reconstruction

This work investigates the positional single photon incidence response（P-SPIR） to provide an accurate point spread function（PSF）-contained system matrix and its incorporation within the image reconstruction framework.Based on the Geant4 Application for Emission Tomography（GATE） simulation,P-SPIR theory takes both incidence angle and incidence position of the gamma photon into account during crystal subdivision,instead of only taking the former into account,as in single photon incidence response（SPIR）.The response distribution obtained in this fashion was validated using Monte Carlo simulations.In addition,two-block penetration and normalization of the response probability are introduced to improve the accuracy of the PSF.With the incorporation of the PSF,the homogenization model is then analyzed to calculate the spread distribution of each line-of-response（LOR）.A primate PET scanner,Eplus-260,developed by the Institute of High Energy Physics,Chinese Academy of Sciences（IHEP）,was employed to evaluate the proposed method.The reconstructed images indicate that the P-SPIR method can effectively mitigate the depth-of-interaction（DOI） effect,especially at the peripheral area of field-of-view（FOV）.Furthermore,the method can be applied to PET scanners with any other structures and list-mode data format with high flexibility and efficiency.

Global stabilization of linear periodically time-varying switched systems via matrix inequalities

In this paper, we address the stabilization problem for linear periodically time-varying switched systems. Using discretization technique, we derive new conditions for the global stabilizability in terms of the solution of matrix inequalities. An algorithm for finding stabilizing controller and switching strategy is presented.

Reflexive solution to a system of matrix equations

We derive necessary and sufficient conditions for the existence and an expression of the （anti）reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equations AX = B and XC = D. The explicit solutions of the approximation problem min x∈Ф ｜｜X - E｜｜F was given, where E is a given complex matrix and Ф is the set of all reflexive （or antireflexive） solutions of the system mentioned above, and ｜｜·｜｜ is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper.

Extremal ranks of the solution to a system of real quaternion matrix equations

In this paper, the maximal and minimal ranks of the solution to a system of matrix equations over H, the real quaternion algebra, were derived. A previous known result could be regarded as a special case of the new result.

On stabilization for a class of nonlinear stochastic time-delay systems:a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.

Dynamic Performance Analysis of the Coupling Shaft System in a Carpet Tufting Machine Utilizing the Transfer Matrix Method

The dynamic performance of the coupling shaft system in a carpet tufting machine is the most critical factor affecting the carpet tufting machine's efficiency,and the product quality of the tufted carpet. To determine how to avoid resonance produced by the coupling shaft system's vibration during the weaving process,the dynamic performance of a coupling shaft system in a carpet tufting machine was analyzed. Focusing on a DHGN801D-400 carpet tufting machine,a dynamic model of coupling shaft system was established by utilizing transfer matrix methodology. On the basis of this model,the natural frequencies and mode shapes of the coupling shaft system were obtained through simulations. The correctness of the theoretical model and the dynamic performance of the coupling shaft system were validated by experiments. The first order natural frequency of the coupling shaft system was close to 600 r / min. A conclusion can thus be drawn that operating the carpet tufting machine near this speed should be avoided as much as possible.

Decoupling Control Research on Test System of Hydraulic Drive Unit of Quadruped Robot Based on Diagonal Matrix Method

The mathematical model of hydraulic drive unit of quadruped robot was built in this paper. According to the coupling characteristics between position control system and force control system, the decoupling control strategy was realized based on diagonal matrix method in AMESim?. The results of simulation show that using diagonal matrix method can achieve the decoupling control effectively and it can achieve the decoupling control more effectively with the method of not offset pole-zero in the S coordinate. This research can provide theoretical basis for the application of test system of hydraulic drive unit.

Dynamic matrix predictive control for a hydraulic looper system in hot strip mills

Controlling the looper height and strip tension is important in hot strip mills because these variables affect both the strip quality and strip threading. Many researchers have proposed and applied a variety of control schemes for this problem, but the increasingly strict market demand for strip quality requires further improvements. This work describes a dynamic matrix predictive control(DMC) strategy that realizes the optimal control of a hydraulic looper multivariable system. Simulation experiments for a traditional controller and the proposed DMC controller were conducted using MATLAB/Simulink software. The simulation results show that both controllers acquire good control effects with model matching. However, when the model is mismatched, the traditional controller produces an overshoot of 32.4% and a rising time of up to 2120.2 ms, which is unacceptable in a hydraulic looper system. The DMC controller restricts the overshoot to less than 0.08%, and the rising time is less than 48.6 ms in all cases.

面向迈创+MatrixZone异构系统的深度学习编程框架

为了满足深度学习模型迭代速度快、算力要求高的需求,主流硬件厂商愈发倾向于采用通用处理器+AI专用加速核的异构系统。但是,由于AI专用加速核仅支持部分核心算子,不具备通用编程能力,如何在这样的异构架构上完成深度学习任务的高效部署值得被深入研究。基于国产自研迈创+MatrixZone异构系统平台,设计并实现了深度学习编程框架KaiSa。KaiSa通过分析深度学习模型输入参数,识别算子类型并划分至对应计算核;对于复杂算子,KaiSa基于性能模型自动完成最优分块大小的搜索,提升双核并行计算的性能。同时,为了实现程序的高效率开发,KaiSa屏蔽了所有的底层硬件细节,给用户提供了一个友好的编程环境。实验结果表明,KaiSa可以获得高达39.0%的性能提升。

ON OPTIMAL BACKWARD PERTURBATION ANALYSIS FOR THE LINEAR SYSTEM WITH BLOCK CYCLIC COEFFICIENT MATRIX

Based on the block style spectral decomposition,this paper deals with the optimal backward perturbation analysis for the linear system with block cyclic coefficient matrix.

A Modified Eigenvector Method for Blind Deconvolution of MIMO Systems Using the Matrix Pseudo-Inversion Lemma

Recently we have developed an eigenvector method (EVM) which can achieve the blind deconvolution (BD) for MIMO systems. One of attractive features of the proposed algorithm is that the BD can be achieved by calculating the eigenvectors of a matrix relevant to it. However, the performance accuracy of the EVM depends highly on computational results of the eigenvectors. In this paper, by modifying the EVM, we propose an algorithm which can achieve the BD without calculating the eigenvectors. Then the pseudo-inverse which is needed to carry out the BD is calculated by our proposed matrix pseudo-inversion lemma. Moreover, using a combination of the conventional EVM and the modified EVM, we will show its performances comparing with each EVM. Simulation results will be presented for showing the effectiveness of the proposed methods.

Research on development of in situ titanium matrix composites and in situ reaction thermodynamics of the reaction systems

The in situ synthesis method for titanium matrix composites （TMCs） has obvious technical and economical advantages over other traditional methods. Ultrafine reinforcement particles were formed in situ by chemical reaction between elements or between elements and compounds. Using the approach, contamination at the composite matrix/reinforcement particle interface did not occur, interface bonding was good, and the reinforcement particle was thermodynamically stable. The stage of development of the preparation process for in situ TMCs as well as the thermodynamic analysis of the possible in situ reaction systems was described.

Observer design for matrix second-order linear systems: a parametric approach

The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.

Design of Luenberger function observer with disturbance decoupling for matrix second-order linear systems-a parametric approach

A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.

Attribute Reduction in Decision Systems Based on Relation Matrix

This paper proposes,from the viewpoint of relation matrix,a new algorithm of attribute reduction for decision systems.Two new and relative reasonable indices are first defined to measure significance of the attributes in decision systems and then a heuristic algorithm of attribute reduction is formulated.Moreover,the time complexity of the algorithm is analyzed and it is proved to be complete.Some numerical experiments are also conducted to access the performance of the presented algorithm and the results demonstrate that it is not only effective but also efficient.

ON THE CONVERGENCE DOMAIN OF THE MATRIX MULTISPLITTING RELAXATION METHODS FOR LINEAR SYSTEMS

The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473 486) is further investigated. The investigations show that these relaxation methods really have considerably larger convergence domains.

Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.