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MVMS-RCN: A Dual-Domain Unified CT Reconstruction with Multi-sparse-view and Multi-scale Refinement-correction

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arXiv 2024年

作者： Fan, Xiaohong Chen, Ke Yi, Huaming Yang, Yin Zhang, Jianping The School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China The Centre for Mathematical Imaging Techniques Department of Mathematical Sciences The University of Liverpool LiverpoolL6972L United Kingdom The School of Mathematics and Computational Science Xiangtan University Hunan National Applied Mathematics Center Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan411105 China

X-ray Computed Tomography (CT) is one of the most important diagnostic imaging techniques in clinical applications. Sparse-view CT imaging reduces the number of projection views to a lower radiation dose and alleviates the potential risk of radiation exposure. Most existing deep learning (DL) and deep unfolding sparse-view CT reconstruction methods: 1) do not fully use the projection data;2) do not always link their architecture designs to a mathematical theory;3) do not flexibly deal with multi-sparse-view reconstruction assignments. This paper aims to use mathematical ideas and design optimal DL imaging algorithms for sparse-view CT reconstructions. We propose a novel dual-domain unified framework that offers a great deal of flexibility for multi-sparse-view CT reconstruction through a single model. This framework combines the theoretical advantages of model-based methods with the superior reconstruction performance of DL-based methods, resulting in the expected generalizability of DL. We propose a refinement module that utilizes unfolding projection domain to refine full-sparse-view projection errors, as well as an image domain correction module that distills multi-scale geometric error corrections to reconstruct sparse-view CT. This provides us with a new way to explore the potential of projection information and a new perspective on designing network architectures. The multi-scale geometric correction module is end-to-end learnable, and our method could function as a plug-and-play reconstruction technique, adaptable to various applications. Extensive experiments demonstrate that our framework is superior to other existing state-of-the-art methods. Our source codes are available at https://***/fanxiaohong/MVMS-RCN. Copyright © 2024, The Authors. All rights reserved.

关键词： Geometry

Nest-DGIL: Nesterov-optimized Deep Geometric Incremental Learning for CS Image Reconstruction

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arXiv 2023年

作者： Fan, Xiaohong Yang, Yin Chen, Ke Feng, Yujie Zhang, Jianping The School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University Hunan National Applied Mathematics Center Xiangtan411105 China The Centre for Mathematical ImagingTechniques Department of Mathematical Sciences The University of Liverpool Department of Mathematics and Statistics University of Strathclyde Glasgow United Kingdom The School of Mathematics and Computational Science Xiangtan University The Key Laboratory of Intelligent Computing & Information Processing The Ministry of Education Xiangtan411105 China

Proximal gradient-based optimization is one of the most common strategies to solve inverse problem of images, and it is easy to implement. However, these techniques often generate heavy artifacts in image reconstruction. One of the most popular refinement methods is to fine-tune the regularization parameter to alleviate such artifacts, but it may not always be sufficient or applicable due to increased computational costs. In this work, we propose a deep geometric incremental learning framework based on the second Nesterov proximal gradient optimization. The proposed end-to-end network not only has the powerful learning ability for high-/low-frequency image features, but also can theoretically guarantee that geometric texture details will be reconstructed from preliminary linear reconstruction. Furthermore, it can avoid the risk of intermediate reconstruction results falling outside the geometric decomposition domains and achieve fast convergence. Our reconstruction framework is decomposed into four modules including general linear reconstruction, cascade geometric incremental restoration, Nesterov acceleration, and post-processing. In the image restoration step, a cascade geometric incremental learning module is designed to compensate for missing texture information from different geometric spectral decomposition domains. Inspired by the overlap-tile strategy, we also develop a post-processing module to remove the block effect in patch-wise-based natural image reconstruction. All parameters in the proposed model are learnable, an adaptive initialization technique of physical parameters is also employed to make model flexibility and ensure converging smoothly. We compare the reconstruction performance of the proposed method with existing state-of-the-art methods to demonstrate its superiority. Our source codes are available at https://***/fanxiaohong/Nest-DGIL. Copyright © 2023, The Authors. All rights reserved.

关键词： Image reconstruction

Adaptive mesh refinement and superconvergence for two-dimensional interface problems

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SIAM Journal on Scientific Computing 2014年第4期36卷 A1478-A1499页

作者： Wei, Huayi Chen, Long Huang, Yunqing Zheng, Bin Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Lab. of Intelligent Comp. and Info. Proc. Comp. Min. of Educ. School of Math. and Computational Sci. Xiangtan University Xiangtan Hunan 411105 China Department of Mathematics University of California at Irvine Irvine 92697 CA United States Northwest National Lab Richland 99352 WA United States

Adaptive mesh refinement and the Börgers algorithm are combined to generate a body-fitted mesh which can resolve the interface with fine geometric details. Standard linear finite element method based on such body-fitted meshes is applied to the elliptic interface problem and proven to be superclose to the linear interpolation of the exact solution. Based on this superconvergence result, a maximal norm error estimate of order one and half is obtained without using the discrete maximum principle. The data structure and meshing algorithms, including local refinement and coarsening, are very simple. In particular, no tree structure is needed. An efficient solver for solving the resulting linear algebraic systems is also developed and shown be robust with respect to both the problem size and the jump of the diffusion coefficients. © 2014 Society for Industrial and Applied Mathematics.

关键词： Adaptive mesh refinement Body-fitted mesh Superconvergence

UNCONDITIONALLY ENERGY STABLE IEQ-FEMS FOR THE CAHN-HILLIARD EQUATION AND ALLEN-CAHN EQUATION

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arXiv 2024年

作者： Chen, Yaoyao Liu, Hailiang Yi, Nianyu Yin, Peimeng School of Mathematics and Statistics Anhui Normal University Anhui Wuhu241000 China Department of Mathematics Iowa State University AmesIA50011 United States Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Department of Mathematical Sciences The University of Texas at El Paso El PasoTX79968 United States

In this paper, we present several unconditionally energy-stable invariant energy quadratization (IEQ) finite element methods (FEMs) with linear, first- and second-order accuracy for solving both the Cahn-Hilliard equation and the Allen-Cahn equation. For time discretization, we compare three distinct IEQ-FEM schemes that position the intermediate function introduced by the IEQ approach in different function spaces: finite element space, continuous function space, or a combination of these spaces. Rigorous proofs establishing the existence and uniqueness of the numerical solution, along with analyses of energy dissipation for both equations and mass conservation for the Cahn-Hilliard equation, are provided. The proposed schemes' accuracy, efficiency, and solution properties are demonstrated through numerical experiments. © 2024, CC BY-NC-ND.

关键词： Finite element method

A directed continuous time random walk model with jump length depending on waiting time

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The Scientific World Journal

The Scientific World Journal 2014年第1期2014卷 182508页

作者： Shi, Long Yu, Zuguo Mao, Zhi Xiao, Aiguo Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China Institute of Mathematics and Physics Central South University of Forest and Technology Changsha Hunan 410004 China School of Mathematical Sciences Queensland University of Technology Brisbane QLD 4001 G.P.O. Box 2434 Australia

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P (x, t) of finding the walker at position x at time t is completely determined by the Laplace transform of the probability density function (t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived. © 2014 Long Shi et al.

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Theory of polygonal phases self-assembled from T-shaped liquid crystalline molecules

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arXiv 2023年

作者： He, Zhijuan Wang, Xin Zhang, Pingwen Shi, An-Chang Jiang, Kai Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Statistics Wuhan University Wuhan430072 China School of Mathematical Sciences Peking University Beijing100871 China Department of Physics and Astronomy McMaster University HamiltonONL8S 4M1 Canada

Extensive experimental studies have shown that numerous ordered phases can be formed via the self-assembly of T-shaped liquid crystalline molecules (TLCMs) composed of a rigid backbone, two flexible end chains and a flexible side chain. However, a comprehensive understanding of the stability and formation mechanisms of these intricately nanostructured phases remains incomplete. Here we fill this gap by carrying out a theoretical study of the phase behaviour of TLCMs. Specifically, we construct phase diagrams of TLCMs by computing the free energy of different ordered phases of the system. Our results reveal that the number of polygonal edges increases as the length of side chain or interaction strength increases, consistent with experimental observations. The theoretical study not only reproduces the experimentally observed phases and phase transition sequences, but also systematically analyzes the stability mechanism of the polygonal phases. Copyright © 2023, The Authors. All rights reserved.

关键词： Free energy

An Improved Third-order CWENO-Z Scheme at critical points

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IOP Conference Series: Materials science and engineering 2019年第3期569卷

作者： Shujiang Tang Mingjun Li Shuang Han School of mathematics and computational science Xiangtan University Xiangtan Hunan 411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan Hunan 411105 China

In this paper, by modifying the smoothness factor of the third-order CWENO scheme, we present the two-parameter CWENO-NZ3 scheme to improve accuracy at critical points. We selected some classical examples for numerical simulation, such as one-dimensional Sod shock tube, Shock-entropy wave interaction, Riemann problem with strong discontinuity and Rayleigh-Taylor instability problem. Numerically comparing with the classical third-order CWENO schemes, it is found that the improved schemes not only improve accuracy and resolution at the extreme points, but also reduce dissipation.

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A convergence analysis of a structure-preserving gradient flow method for the all-electron Kohn-Sham model

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arXiv 2023年

作者： Shen, Yedan Wang, Ting Zhou, Jie Hu, Guanghui School of Mathematics and Information Science Guangzhou University Guangzhou China Faculty of Science and Technology University of Macau China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan China School of Mathematical Computational Sciences Xiangtan University Xiangtan China Zhuhai UM Science & Technology Research Institute Zhuhai China Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications University of Macau China

In [Dai et al, Multi. Model. Simul., 2020], a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn–Sham density functional theory, based on which a linearized method was developed in [Hu, et al, EAJAM, accepted] for further improving the numerical efficiency. In this paper, a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn–Sham model. Temporally, the convergence, the asymptotic stability, as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works, while spatially, the convergence of the h-adaptive mesh method is demonstrated following [Chen et al, Multi. Model. Simul., 2014], with a key study on the boundedness of the Kohn–Sham potential for the all-electron Kohn–Sham model. Numerical examples confirm the theoretical results very well. Copyright © 2023, The Authors. All rights reserved.

关键词： Asymptotic stability

Energy-Efficient Virtual Machine Placement in Data Centers Via Accelerated Genetic Algorithm with Improved Fitness computation

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SSRN

SSRN 2021年

作者： Hormozi, Elham Hu, Shuwen Ding, Zhe Tian, Yu-Chu Wang, You-Gan Yu, Zu-Guo Zhang, Weizhe School of Computer Science Queensland University of Technology GPO Box 2434 BrisbaneQLD4001 Australia School of Mathematical Sciences Queensland University of Technology GPO Box 2434 BrisbaneQLD4001 Australia Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China School of Cyberspace Science Harbin Institute of Technology Harbin China Cyberspace Security Research Center Peng Cheng Laboratory Shenzhen China Queensland University of Technology

Energy efficiency basically refers to how effectively energy can be utilised or consumed by any virtualised data centre giving cloud administrations. Since Genetic Algorithm (GA) is an acceptable method to solve the VM placement problem, this research formulates the Virtual Machine (VM) placement problem as a constrained optimisation problem. A considerable amount of residual resources is available for each new VM allocation, however they are distributed across multiple active PMs, rendering them inefficient. Our research focuses on improving a data centre’s energy and time efficiency by devising a technique to decrease PM’s residual resources and make them more valuable. As the most time consuming element of a GA is calculating the fitness function, this paper presents a new fitness function to simplify the fitness function calculation in GA. The results are compared to the standard GA and First Fit Decreasing (FFD) algorithm. The findings reveals a 8% energy savings for our GA compared to FFD and a 66% reduction in our GA execution time compared to the standard GA for virtualised data centres. The simulation experiments are conducted on small-, medium- and large-scale of the google data centre to demonstrate the effectiveness of our GA. © 2021, The Authors. All rights reserved.

关键词： Energy efficiency