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Spatiotemporal Flexible Sparse Reconstruction for Rapid Dynamic Contrast-Enhanced MRI

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING 2022年第1期69卷 229-243页

作者： Hu, Yuhan Zhang, Xinlin Chen, Dicheng Yan, Zhiping Shen, Xiaoyong Yan, Gen Lin Ou-yang Lin, Jianzhong Dong, Jiyang Qu, Xiaobo Xiamen Univ Natl Model Microelect Coll Fujian Prov Key Lab Plasma & Magnet Resonance Dept Elect SciSch Elect Sci & Engn Xiamen 361105 Peoples R China Fujian Med Univ Xiamen Humanity Hosp Fuzhou Peoples R China Zhejiang Univ Affiliated Hosp 1 Sch Med Hangzhou Peoples R China Xiamen Med Coll Dept Radiol Hosp 2 Xiamen Peoples R China Xiamen Univ Dept Med Imaging Southeast Hosp Med Coll Xiamen Peoples R China Xiamen Univ Magnet Resonance Ctr Zhongshan Hosp Xiamen Peoples R China

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a tissue perfusion imaging technique. Some versatile free-breathing DCE-MRI techniques combining compressed sensing (CS) and parallel imaging with golden-angle radial sampling have been developed to improve motion robustness with high spatial and temporal resolution. These methods have demonstrated good diagnostic performance in clinical setting, but the reconstruction quality will degrade at high acceleration rates and overall reconstruction time remains long. In this paper, we proposed a new parallel CS reconstruction model for DCE-MRI that enforces flexible weighted sparse constraint along both spatial and temporal dimensions. Weights were introduced to flexibly adjust the importance of time and space sparsity, and we derived a fast-thresholding algorithm which was proven to be simple and efficient for solving the proposed reconstruction model. Results on both the brain tumor DCE and liver DCE show that, at relatively high acceleration factor of fast sampling, lowest reconstruction error and highest image structural similarity are obtained by the proposed method. Besides, the proposed method achieves faster reconstruction for liver datasets and better physiological measures are also obtained on tumor images.

关键词： Image reconstruction Analytical models Pipelines Magnetic resonance imaging Hospitals Spatial resolution Sparse matrices DCE-MRI parallel imaging golden-angle radial sampling sparse reconstruction fast algorithm

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fast artificial boundary method for the heat equation on unbounded domains with strip tails

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2023年第1期425卷

作者： Zheng, Chunxiong Xie, Jiangming Xinjiang Univ Coll Math & Syst Sci Urumqi 830046 Peoples R China Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China

We propose a fast numerical algorithm for the multi-dimensional heat equation on unbounded domains with strips tails. The artificial boundary method is used to confine the computational domains. By applying BDF2 for the time discretization and performing the Z transform, we derive an exact semi-discrete artificial boundary condition which contains the discrete temporal convolution and the surface Laplacian operator. Based on the best relative Chebyshev approximation of the square-root function, we design a fast algorithm to approximate and localize the exact semi-discrete artificial boundary condition. The spatial discretization is realized by the Galerkin finite element method with a special boundary treatment. A complete error estimate for the fully discrete problems is performed, and numerical tests are presented to demonstrate the accuracy and efficiency of the proposed algorithm.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Unbounded domains Artificial boundary method fast algorithm Error estimate

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Some Numerical Extrapolation Methods for the Fractional Sub-diffusion Equation and Fractional Wave Equation Based on the L1 Formula

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Communications on Applied Mathematics and Computation 2022年第4期4卷 1313-1350页

作者： Ren-jun Qi Zhi-zhong Sun School of Mathematics Southeast UniversityNanjing 210096JiangsuChina

With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion *** extrapolation formulas are presented,whose temporal convergence orders in L_(∞)-norm are proved to be 2,3-α,and 4-2α,respectively,where 0<α<***,by the method of order reduction,an extrapola-tion method is constructed for the fractional wave equation including two extrapolation formulas,which achieve temporal 4-γ and 6-2γ order in L_(∞)-norm,respectively,where1<γ<*** the derived extrapolation methods with the fast algorithm for Caputo fractional derivative based on the sum-of-exponential approximation,the fast extrapolation methods are obtained which reduce the computational complexity significantly while keep-ing the *** numerical experiments confirm the theoretical results.

关键词： L1 formula Asymptotic expansion Fractional sub-diffusion equation Fractional wave equation Richardson extrapolation fast algorithm

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Two fast numerical methods for a generalized Oldroyd-B fluid model

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2023年 117卷

作者： Bu, Weiping Yang, Huimin Tang, Yifa Xiangtan Univ Sch Math & Computat Sci Xiangtan 411105 Hunan Peoples R China Xiangtan Univ Hunan Key Lab Computat & Simulat Sci & Engn Xiangtan 411105 Hunan Peoples R China Chinese Acad Sci Acad Math & Syst Sci LSEC ICMSEC Beijing 100190 Peoples R China

This work proposes two fast and efficient numerical methods for a generalized Oldroyd-B fluid model with fractional derivatives. The fast evaluations of the Riemann-Liouville fractional derivatives are developed based on convolution quadrature generated by the backward Euler and the second-order backward difference methods. By using these fast algorithms in time and employing the finite element method in space, two fully discrete schemes are established for the considered problem. Further, we discuss the error estimates of these numerical schemes based on the property of the initial value and the right hand function instead of the regularity assumption of the exact solution. Finally, some numerical tests are presented to verify the effectiveness of the numerical schemes and confirm the theoretical results.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Fractional Oldroyd-B fluid model Convolution quadrature fast algorithm Finite element method Error estimate

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Exponential-sum-approximation technique for variable-order time-fractional diffusion equations

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2022年第1期68卷 323-347页

作者： Zhang, Jia-Li Fang, Zhi-Wei Sun, Hai-Wei Univ Macau Dept Math Macau Peoples R China

In this paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO function alpha(t) is an element of (0, 1), we develop an exponential-sum-approximation (ESA) technique to approach the VO Caputo fractional derivative. The ESA technique keeps both the quadrature exponents and the number of exponentials in the summation unchanged at different time level. Approximating parameters are properly selected to achieve the efficient accuracy. Compared with the general direct method, the proposed method reduces the storage requirement from O(n) to O(log(2) n) and the computational cost from O(n(2)) to O(n log(2) n), respectively, with n being the number of the time levels. When this fast algorithm is exploited to construct a fast ESA scheme for the VO time-fractional diffusion equations, the computational complexity of the proposed scheme is only of O(mn log(2) n) with O(m log(2) n) storage requirement, where m denotes the number of spatial grid points. Theoretically, the unconditional stability and error analysis of the fast ESA scheme are given. The effectiveness of the proposed algorithm is verified by numerical examples.

关键词： Variable-order Caputo fractional derivative Exponential-sum-approximation method fast algorithm Time-fractional diffusion equation Stability and convergence

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algorithm for computing all the shortest reducts based on a new pruning strategy

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INFORMATION SCIENCES 2022年 585卷 113-126页

作者： Gonzalez-Diaz, Yanir Martinez-Trinidad, Jose Fco Carrasco-Ochoa, Jesus A. Lazo-Cortes, Manuel S. Inst Nacl Astrofis Opt & Electr Comp Sci Dept Luis Enrique Erro 1 Puebla 72840 Mexico TecNM Inst Tecnol Tlalnepantla Ave Inst Tecnol S-N Tlalnepantla De Baz 54070 Edo Mexico Mexico

ABSTR A C T In this paper, we introduce an algorithm for computing all the shortest reducts in a deci-sion system. The proposed algorithm is based on determining the size of the shortest reducts using a small super-reduct and some new pruning methods. Once the size of the shortest reduct is determined, all other reducts of the same size are found applying the new pruning methods. The results of our experiments using several synthetic and real -world decision systems show that the proposed algorithm is, in most cases, faster than the state of the art algorithms for computing all the shortest reducts reported in the literature. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Shortest reducts Rough sets Decision systems fast algorithm

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A fast temporal second-order compact ADI difference scheme for the 2D multi-term fractional wave equation

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NUMERICAL algorithmS 2021年第2期86卷 761-797页

作者： Sun, Hong Sun, Zhi-zhong Nanjing Inst Technol Dept Math & Phys Nanjing 211167 Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China

In this paper, a fast temporal second-order compact ADI scheme is proposed for the 2D time multi-term fractional wave equation. At the super-convergence point, the multi-term Caputo derivative is approximated by combining the order reduction technique with the sum-of-exponential approximation to the kernel function appeared in Caputo derivative. The difference scheme can be solved by the recursion, which reduces the storage and computational cost significantly. The obtained scheme is uniquely solvable. The unconditional convergence and stability of the scheme in the discrete H-1-norm are proved by the discrete energy method and the convergence accuracy is second-order in time and fourth-order in space. Numerical example illustrates the efficiency of the scheme.

关键词： Fractional wave equation Multi-term fractional derivatives Difference scheme Stability Convergence fast algorithm

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Regularization Particle Size Inversion of PCS Based on fast algorithm 11

Regularization Particle Size Inversion of PCS Based on Fast ...

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11th World Congress on Intelligent Control and Automation

作者： Zhang, Yanmin Li, Qinghua Wang, Lipeng Qi, Xingguang Qilu Univ Technol Sch Elect Engn & Automat Jinan Shandong Peoples R China Shandong Univ Key Lab Adv Mfg & Measurement & Control Technol Jinan Shandong Peoples R China

ISBN: (纸本)9781479958252

Tikhonov regularization is an effective method for particle size inversion of Photon Correlation Spectroscopy (PCS). Regularization parameter selection is the key point of Tikhonov regularization algorithm for solving the first kind integral problem. In order to obtain the optimal regularization parameter, according to the Morozov discrepancy principal, this paper proposes an efficient regularization inversion method based on fast algorithm for implementing the problem of particle size distribution. Computer simulation data of monodisperse particles and bi-dispersed particles are inversed by this method respectively. The inversion results show that, when the noise level is 0 similar to 0.01, inversion results of fast algorithm are reasonable, however, when the noise level is greater than 0.005, discrepancy principal can't obtain correct inversion results. Therefore, Tikhonov regularization inversion method with fast algorithm has the advantages of high accuracy, tolerance of noises and fast speed in PCS inversion.

关键词： PCS Tikhonov regularization algorithm discrepancy principle fast algorithm

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Research on a fast algorithm of Model Predictive Control 11

Research on a Fast Algorithm of Model Predictive Control

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11th World Congress on Intelligent Control and Automation

作者： Pan Hao Yuan Ming-zhe Chinese Acad Sci Shenyang Inst Automat Shenyang 110016 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China

ISBN: (纸本)9781479958252

The traditional control methods are not able to keep control performance in a high level because response speed becomes more important for industrial control. This paper presented a fast predictive control algorithm, which was easy and simple to calculate and the principle of algorithm was very clear and greatly improved the speed of response and calculation, as well as demonstrated the principles of fast algorithms and operation process of the algorithm. Finally, we analyzed the stability, dynamic characteristics and steady state characteristics of system, and used lead-lag correction link to improve the performance of system. The results of simulation demonstrated that all of methods and improved algorithms were feasibility.

关键词： fast algorithm Model Predictive Control Steady-State Analysis Dynamic Analysis Lead-Lag Correction

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A fast algorithm for Motion and Disparity Estimation Based on the Reference Directions of Neighboring Macroblocks

A Fast Algorithm for Motion and Disparity Estimation Based o...

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International Conference on Mechatronics and Semiconductor Materials (ICMSCM 2013)

作者： Kong Xiangjun Zhao Yan Fan Qian Wang Shi-gang Chen Hexin Jilin Univ Coll Commun Engn Changchun 130012 Peoples R China

ISBN: (纸本)9783037859391

As for JMVC (Joint Multi-view Video Coding), when executing motion and disparity estimation simultaneously, the implicit correlation of reference directions between current and neighboring macroblocks is neglected, and this will lead to useless searching. To reduce this redundancy, we propose an estimation algorithm which sets search ranges properly by exploiting the mentioned correlation. The proposed algorithm first gets the reference directions of macroblocks in the left, top and top right direction of current macroblock, and compares them with current reference direction, then sets search ranges by the comparison results, executes motion and disparity estimation in the new ranges at last. Experimental results show that the proposed algorithm can save 28.98%- 46.30% of coding time without degradation of coding quality comparing to JMVC.

关键词： JMVC motion estimation disparity estimation fast algorithm

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