Table of Content

15 June 2024, Volume 41 Issue 3 Previous Issue   

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Sampling Patterns in Accelerating Magnetic Resonance Imaging: a Survey LI Xing, YANG Yan, JING Wenfeng 2024, 41 (3):  397-409.  doi: 10.3969/j.issn.1005-3085.2024.03.001 Abstract ( 105 )   Save Accelerating MRI has been widely used in clinical medicine by reconstruction after undersampling in $k$-space and parallel MRI technology can effectively reduce the scanning time in MRI examination. Driven by deep learning technology which involved in accelerating MRI has made a breakthrough. Accelerating MRI based on deep learning has become the research hotspot in the field of MRI with its faster scanning and imaging. The high quality of MRI images with less artifacts can be reconstructed even with lower sample ratio. In this paper, we first briefly reviews the traditional accelerating MRI sampling methods and then introduce the joint optimization framework of under-sampling and reconstruction based on deep learning in accelerating MRI by comparing the performance of relevant frameworks. Finally, we discuss the development trend of accelerating MRI sampling. Related Articles | Metrics

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Face Recognition Algorithm Based on Convolutional Neural Network with Feature Information YUE Ye, WEN Ruiping, WANG Chuanlong 2024, 41 (3):  410-420.  doi: 10.3969/j.issn.1005-3085.2024.03.002 Abstract ( 128 )   Save In image classification, convolution neural network has made great progress in face recognition. When convolution is used to extract face image feature information, when the number of convolution kernels is limited, the feature values, such as hair, texture, may not represent the main features of the person well, resulting in the reduction of recognition rate. To solve this problem, a face recognition method based on feature information convolution neural network is proposed in this paper. In the process of image processing, ingular value decomposition is used to select the first four singular values to represent the main features of the face, and most of the useless feature information is quickly filtered out. The convolution network can improve the receptive field of the network without losing the information of the feature map, and fuse the most representative feature information. The convolutional neural network model and the structural model of feature fusion based on singular value decomposition are used to realize face recognition. The simulation results show that this method reduces the training time of the algorithm and improves the accuracy of face recognition. Related Articles | Metrics

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A Local Gaussian Distribution Model for Image Registration ZHANG Jing, QUAN Tingting 2024, 41 (3):  421-431.  doi: 10.3969/j.issn.1005-3085.2024.03.003 Abstract ( 64 )   Save This paper proposes a new non-rigid image registration model based on the combination of statistical and variational methods. Assuming that the residual image obeys a local Gaussian distribution with different means and variances, a dual energy functional is obtained. Combined with the variational regularization method, a new registration model is obtained in this paper. The novelty of this method lies in the introduction of weighting functions and some control parameters in the fidelity term. The weighting functions can automatically and effectively distinguish regions with different grayscale contrasts in residual image, and the control parameters improve the robustness of the algorithm. The registration results of synthetic images, two-dimensional lung CT, and three-dimensional brain MRI images demonstrate the effectiveness and accuracy of this method. Related Articles | Metrics

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A Generalized Golub-Kahan Bidiagonalization Regularization Method for Large Discrete Ill-posed Problems YANG Siyu, WANG Zhengsheng, LI Wei, XU Guili 2024, 41 (3):  432-446.  doi: 10.3969/j.issn.1005-3085.2024.03.004 Abstract ( 68 )   Save Ill-posed problems arise in many areas of science and engineering. Their solutions, if they exist, are very sensitive to perturbations in the data. In order to reduce this sensitivity, typically, regularization methods replace the original problem by a minimization problem with a fidelity term and a regularization term and are popularly used to solve the ill-posed problems. Recently, the use of a $p$-norm to measure the fidelity term, and a $q$-norm to measure the regularization term, has received considerable attention. This paper presents a new efficient approach for the solution of the $p$-norm and $q$-norm minimization model of large discrete ill-posed problems, based on the majorization-minimization framework and the Golub-Kahan Lanczos bidiagonalization process, by using the discrepancy principle to choose the regularization parameters, called Majorization-Minimization Generalized Golub-Kahan Lanczos bidiagonalization regularization method (MM-GKL). The proof of the convergence analysis is provided. Numerical experiments illustrate that the proposed new method is more effective and less computational cost than the existing methods. Computed image restoration examples illustrate that it suffices to carry out less computational cost to achieve higher quality restorations. The combination of a low iteration count and a less computational cost requirement makes the proposed method attractive. Related Articles | Metrics

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Global Dynamics of a Reaction-diffusion Malaria Model with Seasonality ZHANG Zhiwen, BAI Zhenguo 2024, 41 (3):  447-457.  doi: 10.3969/j.issn.1005-3085.2024.03.005 Abstract ( 62 )   Save Malaria is an infectious disease caused by the Plasmodium parasite and it is transmitted among humans through bites of adult female Anopheles mosquitoes. To investigate the effects of spatial heterogeneities and seasonality, we develop a periodic reaction-diffusion model. Since the total density of mosquitoes tends to be a positive periodic solution, we are focus on the limiting system associated with the original system. We first introduce the basic reproduction number $\mathcal {R}_0$ and then show that $\mathcal {R}_0$ serves as a threshold parameter in determining the global dynamics of the limiting system by employing the theory of monotone and subhomogeneous systems. More precisely, the disease-free periodic solution is globally asymptotically stable if $\mathcal {R}_0\leq 1$, and the model admits a unique positive periodic solution that is globally asymptotically stable when $\mathcal {R}_0>1$. Finally, the threshold type result for the limiting system is lifted to the original system with the help of the theory of chain transitive sets. Related Articles | Metrics

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Dynamic Analysis of the COVID-19 Epidemic Model with Vaccination and Environmental Transmission WANG Xiaojing, LI Jiahui, YAN Huilin, GUO Songbai, LIANG Yu, CHEN Jingyi 2024, 41 (3):  458-468.  doi: 10.3969/j.issn.1005-3085.2024.03.006 Abstract ( 53 )   Save Based on the method of mathematical modeling of infectious disease dynamics and the transmission mechanism of COVID-19, an SEIARW epidemic model is established, which incorporating vaccination and environmental transmission. Firstly, the control reproduction number of the model is calculated, and then the existence and uniqueness of the endemic equilibrium are given. Furthermore, two Lyapunov functions are constructed to prove the global stability of both the disease-free equilibrium and the endemic equilibrium. Finally, numerical simulations have been carried out to draw variation lines of the control reproduction number corresponding to its parameters and to fit the epidemic data of symptomatic in Beijing from November 20 to December 5, 2022. The results show that increasing vaccination coverage and vaccine effectiveness can reduce the final size and strengthening the elimination of virus in the environment can effectively reduce the number of the exposed, asymptomatic and symptomatic. Meanwhile, scientific prevention and control strategies should be formulated according to local conditions to avoid excessive disinfection damaging human health and polluting the environment. Related Articles | Metrics

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Qualitative Analysis of Stochastic SIRS Epidemic Model with Logistic Growth and Psychological Effect ZHAO Yanjun, SU Li, SUN Xiaohui, LI Wenxuan 2024, 41 (3):  469-480.  doi: 10.3969/j.issn.1005-3085.2024.03.007 Abstract ( 78 )   Save Based on the fact that epidemics are affected by environmental noise and psychological effects, a stochastic SIRS epidemic model with Logistic growth and psychological effects is established to discuss the effects of Logistic growth and psychological effects on the global dynamics of the model. Firstly, by constructing the Lyapunov function and using the It$\hat{\rm o}$ formula, the existence and uniqueness of the global positive solution of the model are proved, and then, under appropriate conditions, by using the random Lyapunov function method, the sufficient conditions for the existence of ergodic stationary distribution of the positive solution of the model are obtained by using the LaSalle invariance principle. The results show that environmental and psychological change can inhibit the disease under certain conditions. Finally, the correctness of the theoretical results is verified by numerical simulation. Related Articles | Metrics

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A Parameterized Single-step HSS Iteration Method for Continuous Sylvester Matrix Equations MA Changfeng 2024, 41 (3):  481-493.  doi: 10.3969/j.issn.1005-3085.2024.03.008 Abstract ( 58 )   Save The numerical algorithm of continuous Sylvester matrix equation is studied deeply, and a parameterized single step HSS iteration method is proposed innovatively. This method has a unique solution idea and its convergence is proved. In order to improve the performance, quasi-optimal parameters are found by minimizing the upper bound of the spectral radius of the iterative matrix. Numerical experiments verify the effectiveness and robustness of the new method, and demonstrate its high efficiency and stability in solving continuous Sylvester matrix equations, which provides a new tool for relevant numerical calculation. Related Articles | Metrics

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A New Class of Single Parameter F-C Functions and Its Application LI Shuo, SHANG Youlin, QU Deqiang 2024, 41 (3):  494-506.  doi: 10.3969/j.issn.1005-3085.2024.03.009 Abstract ( 61 )   Save The filled function method, as an effective approach for solving global optimization problems involving multivariable and multimodal functions, finds the global optimal solution or approximate global optimal solution by alternately minimizing the objective function and the filled function. Its optimization performance is directly related to the properties of the filled function employed. Consequently, constructing novel filled functions with good mathematical properties has always been a significant hot research. However, existing filled functions present the following issues: they with discontinuity and non-differentiability are not easily solvable; they contain many parameters that are difficult to control and adjust; they include exponential or logarithmic terms affecting the efficiency of the algorithm. To address these shortcomings, the F-C function for solving unconstrained global optimization problems is introduced by combining the filled function with the cross function. Based on this definition, a new single-parameter F-C function is constructed, and the parameter is easily adjustable during the iterative process. By the theoretical properties analysis, a new global optimization F-C function method using the F-C function is proposed, which breaks the solving framework of traditional filled function algorithms, reduces the numbers of solving the objective function, and improves computational efficiency. The effectiveness and feasibility of the F-C function algorithm are verified through several numerical computations. Finally, the F-C function algorithm is applied to optimize parameters in cutting temperature experiments. The numerical experiment results showed that the proposed algorithm has better fitting effect compared with previous findings. Related Articles | Metrics

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Splitting Iterative Methods for Minimizing a Class of Matrix Trace Function in Multivariate Statistical Analysis DUAN Qiang, ZHOU Xuelin, LI Jiaofen 2024, 41 (3):  507-524.  doi: 10.3969/j.issn.1005-3085.2024.03.010 Abstract ( 50 )   Save In this paper, we considered a class of matrix trace function minimization problem under orthogonal constraints which arise in multivariate statistical analysis. Serval special forms of the considered problem model are widely used in the least square fitting of DEDICOM model and orthogonal INDSCAL model in multidimensional scaling analysis. Combining with orthogonal splitting techniques, several classical unfeasible iterative algorithms for solving manifold optimization problems are constructed to solve the underlying problem, and the iterative framework of these algorithms and the specific solution scheme of the generated subproblems are given. Some numerical tests are given to show the efficiency of the proposed methods. Related Articles | Metrics

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ELECTRE II Decision Making Method Based on Interval-valued Pythagorean Hesitant Fuzzy Entropy and Cross Entropy YANG Wei, LI Jing 2024, 41 (3):  525-539.  doi: 10.3969/j.issn.1005-3085.2024.03.011 Abstract ( 46 )   Save In view of the multi-attribute decision problem in which attribute weights are completely unknown or partially known and attribute values are in the form of interval-valued Pythagorean hesitant fuzzy numbers, ELECTRE II decision making method is proposed based on interval-valued Pythagorean hesitant fuzzy entropy and cross entropy. Firstly, new interval score function and interval accuracy function of interval-valued Pythagorean hesitant fuzzy number are defined, and a new distance measure is defined. Secondly, the entropy and cross entropy formula are given based on the fuzzy factor, intuitive factor and amplitude factor of interval-valued Pythagorean hesitant fuzzy number, and their properties are proved. A method to determine attribute weights based on entropy and cross entropy is proposed. Finally, interval-valued Pythagorean hesitation fuzzy ELECTRE II method is proposed, and comprehensive precedence value is used to rank alternatives. The feasibility and effectiveness of the proposed method are verified by numerical example and comparative analysis. Related Articles | Metrics

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Coordinated Exactly Consensus of Multi-agent Systems under Different Topologies of Position and Velocity LI Junhui 2024, 41 (3):  540-550.  doi: 10.3969/j.issn.1005-3085.2024.03.012 Abstract ( 48 )   Save The paper proposes a coordinated iterative learning control protocol for a class of second-order leader-follower nonlinear multi-agent system under the different states communication graphs, a sufficient condition of the exact consensus on a finite time interval for the multi-agent system is also given. Furthermore, the proposed scheme is extended to solve the exact formation control problem on a finite time interval for the multi-agent system. The protocols can reduce the communication cost. The efficiency of the proposed methods are illustrated by two simulation examples. The results show that the MAS could obtain the exact consensus and form a desired formation on the finite-time interval under the conditions that the topology of the velocity is connected although the topology of the position is not necessary connected, the communication requirement is relaxed. It provides an efficient approach in the unmanned aerial vehicles formation problem. Related Articles | Metrics

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Robust Asset-liability Investment Game with Time Delay under Partial Information YANG Lu, ZHANG Chengke, ZHU Huainian, XU Meng 2024, 41 (3):  551-567.  doi: 10.3969/j.issn.1005-3085.2024.03.013 Abstract ( 37 )   Save This paper discusses the robust asset-liability management problem of maximizing the expected utility of the terminal wealth under partial information with delay, that is, the investors can observe the risky asset price with random drift which is not directly observable in the financial market. It is reduced to a partially observed stochastic differential game problem. This paper tries to an effort to find the equilibrium strategies by maximizing the expected utility of the insurer's terminal wealth with delay under the worst-case scenario of the alternative measures. By using the idea of filtering theory and the dynamic programming approach, we derive the robust equilibrium strategies and value functions explicitly. Finally, some numerical examples are presented. Obviously, the value function is higher in the full information case than it in the partial information case. Therefore, investors should collect more information related to investment as much as possible in order to make more informed decisions. Related Articles | Metrics

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The Decomposability of Unbounded Block Operator Matrices and Its Application WANG Xiaoli, Alatancang 2024, 41 (3):  568-576.  doi: 10.3969/j.issn.1005-3085.2024.03.014 Abstract ( 41 )   Save Unbounded block operator matrix widely appears in the fields of system theory, nonlinear analysis and evolution equation problems, and has been widely concerned in both theory and practical application. Firstly, the decomposability of unbounded block operator matrix is characterized by using local spectrum theory. Secondly, the condition that the decomposability of operator matrix remains diagonally stable is given, and some local spectral properties of block operator matrix are generalized and obtained. Finally, as an application, the decomposability of Hamilton operator is investigated and illustrated with examples. Related Articles | Metrics

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Feedback Stabilization of the Self-oscillatory System Based on Washout Filter Algorithm CHAI Xinming, YI Yunfan, ZHAI Chi 2024, 41 (3):  577-586.  doi: 10.3969/j.issn.1005-3085.2024.03.015 Abstract ( 46 )   Save Considering the self-oscillating system evolved from Andronov-Hopf bifurcation and the corresponding linearized system no longer share the same differential manifold, but would exhibit multi-dimensional nonlinear coupling characteristics. Previous study adopts Washout filter to stabilize the oscillatory system, while, the number of filters needed for a particular system is still unsolved. Based on normal form analysis of the Andronov-Hopf bifurcation system, this work explores to connect two filters on the dual-unstable eigenspace, however, feedback design based on state-space method may cause the results being high ordered, which cannot be realized by a Washout filter compartment physically. Through transient dynamics analysis on the Laplace transfer function, we propose to decouple the feedback loop and reduce the Washout algorithm to 1-ordered, which is able to be realized by stable Washout filters physically. A simulation example of the self-oscillation reaction process further verifies the fea-sibility and effectiveness of the obtained control scheme. Related Articles | Metrics

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Newton Iterative Methods for a Class of Quadratic Matrix Equations and Its Convergence LIU Landong, LIU Ming 2024, 41 (3):  587-594.  doi: 10.3969/j.issn.1005-3085.2024.03.016 Abstract ( 49 )   Save Quadratic matrix equation is an important kind of equations in scientific and engineering computations, and it is a meaningful work to explore some effective numerical methods. A special class of quadratic matrix equations derived from quasi-birth-death processes is studied. The quasi-birth-death process has important applications in many fields such as stock price simulation, inventory control, queuing theory, etc. Under the assumption that the minimum non-negative solution exists and is unique, the Newton iteration method is proposed and its convergence is proved. When the initial matrix is zero matrix, the matrix sequence generated by Newton iteration method converges to the unique minimum non-negative solution. Finally, numerical examples are used to verify the effectiveness and feasibility of the algorithm. Related Articles | Metrics