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first-order primal-dual algorithm for sparse-view neutron computed tomography-based three-dimensional image reconstruction

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Nuclear Science and Techniques 2023年第8期34卷 35-53页

作者： Yang Liu Teng-Fei Zhu Zhi Luo Xiao-Ping Ouyang School of Nuclear Science and Engineering North China Electric Power UniversityBeijing 102206China State Key Laboratory of Nuclear Resources and Environment East China University of TechnologyNanchang 330013China State Key Laboratory of Intense Pulsed Radiation Simulation and Effect Xi’an 710024China

Neutron computed tomography(NCT)is widely used as a noninvasive measurement technique in nuclear engineering,thermal hydraulics,and cultural *** neutron source intensity of NCT is usually low and the scan time is long,resulting in a projection image containing severe *** reduce the scanning time and increase the image reconstruction quality,an effective reconstruction algorithm must be *** CT image reconstruction,the reconstruction algorithms can be divided into three categories:analytical algorithms,iterative algorithms,and deep *** the analytical algorithm requires complete projection data,it is not suitable for reconstruction in harsh environments,such as strong radia-tion,high temperature,and high *** learning requires large amounts of data and complex models,which cannot be easily deployed,as well as has a high computational complexity and poor ***,this paper proposes the OS-SART-PDTV iterative algorithm,which uses the ordered subset simultaneous algebraic reconstruction technique(OS-SART)algorithm to reconstruct the image and the first-order primal–dual algorithm to solve the total variation(PDTV),for sparse-view NCT three-dimensional *** novel algorithm was compared with other algorithms(FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV)by simulating the experimental data and actual neutron projection *** reconstruction results demonstrate that the proposed algorithm outperforms the FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV algorithms in terms of preserving edge structure,denoising,and suppressing artifacts.

关键词： NCT first-order primal-dual algorithm OS-SART Total variation Sparse-view

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A first-order inexact primal-dual algorithm for a class of convex-concave saddle point problems

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NUMERICAL algorithmS 2021年第3期88卷 1109-1136页

作者： Jiang, Fan Wu, Zhongming Cai, Xingju Zhang, Hongchao Nanjing Normal Univ Sch Math Sci Jiangsu Key Lab NSLSCS Nanjing 210023 Peoples R China Nanjing Univ Informat Sci & Technol Sch Management Sci & Engn Nanjing 210044 Peoples R China Louisiana State Univ Dept Math Baton Rouge LA 70803 USA

In this paper, we study a first-order inexact primal-dual algorithm (I-PDA) for solving a class of convex-concave saddle point problems. The I-PDA, which involves a relative error criterion and generalizes the classical PDA, has the advantage of solving one subproblem inexactly when it does not have a closed-form solution. We show that the whole sequence generated by I-PDA converges to a saddle point solution with 0(1/N) ergodic convergence rate, where N is the iteration number. In addition, under a mild calmness condition, we establish the global Q-linear convergence rate of the distance between the iterates generated by I-PDA and the solution set, and the R-linear convergence speed of the nonergodic iterates. Furthermore, we demonstrate that many problems arising from practical applications satisfy this calmness condition. Finally, some numerical experiments are performed to show the superiority and linear convergence behaviors of I-PDA.

关键词： Convex optimization Saddle point problems first-order primal-dual algorithm Inexact Nonergodic convergence Linear convergence

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Unified linear convergence of first-order primal-dual algorithms for saddle point problems

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OPTIMIZATION LETTERS 2022年第6期16卷 1675-1700页

作者： Jiang, Fan Wu, Zhongming Cai, Xingju Zhang, Hongchao Nanjing Univ Informat Sci & Technol Sch Math & Stat Dept Informat & Comp Sci Nanjing 210044 Peoples R China Nanjing Univ Informat Sci & Technol Sch Management Sci & Engn Nanjing 210044 Peoples R China Nanjing Normal Univ Sch Math Sci Jiangsu Key Lab NSLSCS Nanjing 210023 Peoples R China Louisiana State Univ Dept Math Baton Rouge LA 70803 USA

In this paper, we study the linear convergence of several well-known first-order primal-dual methods for solving a class of convex-concave saddle point problems. We first unify the convergence analysis of these methods and prove the O(1/N) convergence rates of the primal-dual gap generated by these methods in the ergodic sense, where N counts the number of iterations. Under a mild calmness condition, we further establish the global Q-linear convergence rate of the distances between the iterates generated by these methods and the solution set, and show the R-linear rate of the iterates in the nonergodic sense. Moreover, we demonstrate that the matrix games, fused lasso and constrained TV-l(2) image restoration models as application examples satisfy this calmness condition. Numerical experiments on fused lasso demonstrate the linear rates for these methods.

关键词： first-order primal-dual algorithm Saddle point problem Convex optimization Linear convergence rate

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APPROXIMATE first-order primal-dual algorithmS FOR SADDLE POINT PROBLEMS

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MATHEMATICS OF COMPUTATION 2021年第329期90卷 1227-1262页

作者： Jiang, Fan Cai, Xingju Wu, Zhongming Han, Deren Nanjing Normal Univ Sch Math Sci Jiangsu Key Lab NSLSCS Nanjing 210023 Peoples R China Nanjing Univ Informat Sci & Technol Sch Management Sci & Engn Nanjing 210044 Peoples R China Beihang Univ Sch Math Sci LMIB Beijing 100191 Peoples R China

We propose two approximate versions of the first-order primaldual algorithm (PDA) to solve a class of convex-concave saddle point problems. The introduced approximate criteria are easy to implement in the sense that they only involve the subgradient of a certain function at the current iterate. The first approximate PDA solves both subproblems inexactly and adopts the absolute error criteria, which are based on non-negative summable sequences. Assuming that one of the PDA subproblems can be solved exactly, the second approximate PDA solves the other subproblem approximately and adopts a relative error criterion. The relative error criterion only involves a single parameter in the range of [0, 1), which makes the method more applicable. For both versions, we establish the global convergence and O(1/N) convergence rate measured by the iteration complexity, where N counts the number of iterations. For the inexact PDA with absolute error criteria, we show the accelerated O(1/N-2) and linear convergence rate under the assumptions that a part of the underlying functions and both underlying functions are strongly convex, respectively. Then, we prove that these inexact criteria can also be extended to solve a class of more general problems. Finally, we perform some numerical experiments on sparse recovery and image processing problems. The results demonstrate the feasibility and superiority of the proposed methods.

关键词： first-order primal-dual algorithm saddle point problems convex optimization inexact criteria global convergence

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Inexact first-order primal-dual algorithms

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2020年第2期76卷 381-430页

作者： Rasch, Julian Chambolle, Antonin Westfalische Wilhelms Univ WWU Munster Appl Math Munster Inst Anal & Computat Math Munster Germany CNRS Ecole Polytech CMAP Paris France

We investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors in the proximal maps and gradients. We study several types of errors and show that, provided a sufficient decay of these errors, the same convergence rates as for the error-free algorithm can be established. More precisely, we prove the (optimal) O(1/N) convergence to a saddle point in finite dimensions for the class of non-smooth problems considered in this paper, and prove a O1/N2 or even linear ON convergence rate if either the primal or dual objective respectively both are strongly convex. Moreover we show that also under a slower decay of errors we can establish rates, however slower and directly depending on the decay of the errors. We demonstrate the performance and practical use of the algorithms on the example of nested algorithms and show how they can be used to split the global objective more efficiently.

关键词： first-order primal-dual algorithm Inexact proximal operator Nested algorithms Convex optimization

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Forecasting air pollution PM2.5 in Beijing using weather data and multiple kernel learning

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JOURNAL OF FORECASTING 2020年第2期39卷 117-125页

作者： Xu, Xiang Shanghai Jiao Tong Univ Antai Coll Econ & Management 1954 Huashan Rd Shanghai 200030 Peoples R China

PM2.5 mass concentration prediction is an important research issue because of the increasing impact of air pollution on the urban environment. In this paper, a PM2.5 forecasting framework incorporating meteorological factors based on multiple kernel learning (MKL) is proposed to forecast the near future PM2.5. In addition, we develop a novel two-step algorithm for solving the primal MKL problem. Compared with most existing MKL 2-step algorithms, the proposed algorithm does not require the optimal step size for updating kernel combination coefficients by linear search. To demonstrate the performance of the proposed forecasting framework, its performance is compared to single kernel-based support vector regression (SVR). Data sets of an inland city Beijing acquired from UCI are used to train and validate both of two methods. Experiments show that our proposed method outperforms the SVR.

关键词： first-order primal-dual algorithm meteorological factors multiple kernel learning PM2.5 forecasting

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