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Timesaving phase retrieval approach based on difference map normalization and fast iterative algorithm

OPTICS AND LASERS IN ENGINEERING 2019年第Oct.期121卷 18-28页

作者： Zhang, Yu Tian, Xiaobo Liang, Rongguang Northeast Elect Power Univ Coll Sci Inst Mat Phys Jilin 132012 Jilin Peoples R China Chinese Acad Sci Changchun Inst Opt Fine Mech & Phys State Key Lab Appl Opt Changchun 130022 Jilin Peoples R China Univ Arizona Coll Opt Sci Tucson AZ 85721 USA

To achieve high measurement accuracy with less computational time in phase shifting interferometry, a random phase retrieval approach based on difference map normalization and fast iterative algorithm (DN&FIA) is proposed, it doesn't need pre-filtering, and has the advantage of the iterative algorithms-high accuracy, moreover, it also has the advantage of non-iterative algorithms-timesaving, it only needs three randomly phase shifted interferograms, and the initial phase shifts of the iteration can be random, last but not least, it is effective for the circular, straight or complex fringes. The simulations and experiments verify the correctness and feasibility of DN&FIA.

关键词： Phase shifting algorithm iterative algorithm Difference map normalization Phase shift Interferometry

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Finite iterative algorithm for the symmetric periodic least squares solutions of a class of periodic Sylvester matrix equations

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NUMERICAL algorithmS 2019年第1期81卷 377-406页

作者： Huang, Baohua Ma, Changfeng Fujian Normal Univ Coll Math & Informat Fuzhou 350117 Fujian Peoples R China Fujian Normal Univ FJKLMAA Fuzhou 350117 Fujian Peoples R China

The present work proposes a finite iterative algorithm to find the least squares solutions of periodic matrix equations over symmetric -periodic matrices. By this algorithm, for any initial symmetric -periodic matrices, the solution group can be obtained in finite iterative steps in the absence of round-off errors, and the solution group with least Frobenius norm can be obtained by choosing a special kind of initial matrices. Furthermore, in the solution set of the above problem, the unique optimal approximation solution group to a given matrix group in the Frobenius norm can be derived by finding the least Frobenius norm symmetric -periodic solution of a new corresponding minimum Frobenius norm problem. Finally, numerical examples are provided to illustrate the efficiency of the proposed algorithm and testify the conclusions suggested in this paper.

关键词： Periodic matrix equations iterative algorithm Symmetric -periodic solution Least Frobenius norm Finite number of iterations Optimal approximation solution

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A self-adaptive iterative algorithm for the split common fixed point problems

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NUMERICAL algorithmS 2019年第3期82卷 1047-1063页

作者： Zhao, Jing Hou, Dingfang Civil Aviat Univ China Coll Sci Tianjin 300300 Peoples R China

In this paper, we use the dual variable to propose a self-adaptive iterative algorithm for solving the split common fixed point problems of averaged mappings in real Hilbert spaces. Under suitable conditions, we get the weak convergence of the proposed algorithm and give applications in the split feasibility problem and the split equality problem. Some numerical experiments are given to illustrate the efficiency of the proposed iterative algorithm. Our results improve and extend the corresponding results announced by many others.

关键词： Split common fixed-point problem iterative algorithm Dual variable Averaged mapping Weak convergence Hilbert space

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An iterative algorithm for solving split equality fixed point problems for a class of nonexpansive-type mappings in Banach spaces

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NUMERICAL algorithmS 2019年第3期82卷 987-1007页

作者： Chidume, C. E. Romanus, O. M. Nnyaba, U., V African Univ Sci & Technol Abuja Nigeria

In this paper, an iterative algorithm that approximates solutions of split equality fixed point problems (SEFPP) for quasi-phi-nonexpansive mappings is constructed. Weak convergence of the sequence generated by this algorithm is established in certain real Banach spaces. The theorem proved is applied to solve split equality problem, split equality variational inclusion problem, and split equality equilibrium problem. Finally, some numerical examples are given to demonstrate the convergence of the algorithm. The theorems proved improve and complement a host of important recent results.

关键词： Quasi-phi-nonexpansive mappings Split equality fixed point problem iterative algorithm

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Convergence Characterization of an iterative algorithm for Continuous Coupled Lyapunov Matrix Equations 38

Convergence Characterization of an Iterative Algorithm for C...

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38th Chinese Control Conference (CCC)

作者： You, Shun-Qiang Zhang, Ying Wu, Ai-Guo Harbin Inst Technol Shenzhen 518055 Peoples R China

ISBN: (纸本)9789881563972

In this paper, the convergence characterization of a special implicit iterative algorithm with a tuning parameter for continuous coupled Markov jump Lyapunov matrix equation is investigated. First, a necessary condition for the convergence of the iterative algorithm is given. Then, a necessary and sufficient condition is proposed and the optimal tuning parameter such that the algorithm has the fastest convergence rate is analyzed in two cases according to the distribution of eigenvalues. Finally, a numerical example is given to illustrate the effectiveness of the algorithm and the effects of different tuning parameters.

关键词： Continuous coupled Markov jump Lyapunov matrix equation iterative algorithm convergence condition optimal tuning parameter

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Mixed-Norm Projection-Based iterative algorithm for Face Recognition 16th

Mixed-Norm Projection-Based Iterative Algorithm for Face Rec...

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16th International Symposium on Neural Networks (ISNN)

作者： Liu, Qingshan Xiong, Jiang Yang, Shaofu Southeast Univ Sch Math Nanjing 210096 Peoples R China Chongqing Three Gorges Univ Key Lab Intelligent Informat Proc & Control Chong Chongqing 404100 Wanzhou Peoples R China Southeast Univ Sch Comp Sci & Engn Nanjing 210096 Peoples R China

ISBN: (纸本)9783030228088;9783030228071

In this paper, the mixed-norm optimization is investigated for sparse signal reconstruction. Furthermore, an iterative optimization algorithm based on the projection method is presented for face recognition. From the theoretical point of view, the optimality and convergence of the proposed algorithm is strictly proved. And from the application point of view, the mixed norm combines the L-1 and L-2 norms to give a sparse and collaborative representation for pattern recognition, which has higher recognition rate than sparse representation algorithms. The algorithm is designed by combining the projection operator onto a box set with the projection matrix, which is effective to guarantee the feasibility of the optimal solution. Moreover, numerical experiments on randomly generated signals and three face image data sets are presented to show that the mixed-norm minimization is a combination of sparse representation and collaborative representation for pattern classification.

关键词： Mixed norm Projection method iterative algorithm Face recognition

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An iterative exact algorithm for the weighted fair sequences problem

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COMPUTERS & OPERATIONS RESEARCH 2022年 148卷

作者： Sinnl, Markus Johannes Kepler Univ Linz Inst Prod & Logist Management JKU Business Sch Linz Austria

In this work, we present a new iterative exact solution algorithm for a recently introduced NP-hard sequencing problem. In the problem we are given an upper bound on the allowed solution sequence length and a list of symbols. For each symbol, there is a positive weight and a number, which gives the minimum amount of times the symbol has to occur in a feasible solution sequence. The goal is to find a feasible sequence, which minimizes the maximum weight-distance product, which is calculated for each consecutive appearance of each symbol in the sequence, including the last and first appearance in the sequence, i.e., the sequence is considered to be circular for the calculation of the objective function. Our proposed solution algorithm is based on a new mixed-integer programming model for the problem with a fixed sequence length. We also present various enhancements for our algorithm. We conduct a computational study on the instances from literature to assess the efficiency of our newly proposed solution *** approach solves 404 of 440 instances to optimality within the given time limit, most of them within five minutes. The previous best existing solution approach for the problem only solves 229 of these instances and its exactness depends on an unproven conjecture. Moreover, our approach is up to two orders of magnitude faster compared to this best existing solution approach.

关键词： Scheduling problem Mixed-integer programming Sequencing problem iterative algorithm

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An iterative reconstruction algorithm without system matrix for EPR imaging

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JOURNAL OF MAGNETIC RESONANCE 2022年 344卷 107307页

作者： Qiao, Zhiwei Lu, Yang Liu, Peng Epel, Boris Halpern, Howard Shanxi Univ Sch Comp & Informat Technol Taiyuan 030006 Shanxi Peoples R China Shanxi Inst Technol Dept Big Data & Intelligent Engn Yangquan 045000 Shanxi Peoples R China Univ Chicago Dept Radiat & Cellular Oncol Chicago IL 60637 USA

Electron paramagnetic resonance (EPR) imaging is an advanced oxygen imaging modality for oxygen -image guided radiation. The iterative reconstruction algorithm is the research hot-point in image recon-struction for EPR imaging (EPRI) for this type of algorithm may incorporate image-prior information to construct advanced optimization model to achieve accurate reconstruction from sparse-view projections and/or noisy projections. However, the system matrix in the iterative algorithm needs complicated cal-culation and needs huge memory-space if it is stored in memory. In this work, we propose an iterative reconstruction algorithm without system matrix for EPRI to simplify the whole iterative reconstruction process. The function of the system matrix is to calculate the projections, whereas the function of the transpose of the system matrix is to perform backprojection. The existing projection and backprojection methods are all based on the configuration that the imaged-object remains stationary and the scanning device rotates. Here, we implement the projection and backprojection operations by fixing the scanning device and rotating the object. Thus, the core algorithm is only the commonly-used image-rotation algo-rithm, while the calculation and store of the system matrix are avoided. Based on the idea of image rota-tion, we design a specific iterative reconstruction algorithm for EPRI, total variation constrained data divergence minimization (TVcDM) algorithm without system matrix, and named it as image-rotation based TVcDM (R-TVcDM). Through a series of comparisons with the original TVcDM via real projection data, we find that the proposed algorithm may achieve similar reconstruction accuracy with the original one. But it avoids the complicated calculation and store of the system matrix. The insights gained in this work may be also applied to other imaging modalities, for example computed tomography and positron emission tomography. (c) 2022 Elsevier Inc. All rights r

关键词： iterative algorithm System matrix Image rotation Optimization EPR imaging

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An iterative algorithm to eliminate edges for traveling salesman problem based on a new binomial distribution: Eliminating edges for TSP

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APPLIED INTELLIGENCE 2018年第11期48卷 4470-4484页

作者： Wang, Yong Remmel, Jeffrey B. North China Elect Power Univ Sch Renewable Energy 2 Beinong Rd Huilongguan Beijing 102206 Peoples R China Univ Calif San Diego Dept Math La Jolla CA 92093 USA

Traveling salesman problem (TSP) is one of the extensively studied NP-hard problems. The recent research showed that the TSP on sparse graphs could be resolved in the relatively shorter computation time than that on the complete graph K-n. This paper updates a previous probability model for the optimal Hamiltonian cycle edges according to the frequency quadrilaterals in Kn. A new binomial distribution for TSP is rebuilt to show the probability that an edge e has the frequency 5 in a frequency quadrilateral. Based on the binomial distribution, an iterative algorithm is designed to compute the sparse graphs for TSP. There are two steps at each computation cycle. Firstly, N frequency quadrilaterals containing an edge e in the input graph is chosen to compute the average frequency (f) over bar (e) with the frequency quadrilaterals where e has the frequency 5. Secondly, half edges with the small values (f) over bar (e) are eliminated. The two steps are repeated until a sparse graph is computed. The computation time of the algorithm is O(Nn(2)). For the TSP instances in the TSPLIB, the experimental results illustrated that the sparse graphs with the O(n log(2)n) edges are computed and the original optimal solution is preserved. The experiments means the optimal Hamiltonian cycle edges have the bigger average frequency (f) over bar (e) in K-n and the subgraphs of K-n so they are preserved in the computation process.

关键词： Traveling salesman problem Binomial distribution Frequency quadrilateral iterative algorithm Sparse graph

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Variational Bayesian-Based iterative algorithm for ARX Models with Random Missing Outputs

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2018年第4期37卷 1594-1608页

作者： Chen, Jing Liu, Yanjun Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Peoples R China

In this paper, a variational Bayesian (VB)-based iterative algorithm for ARX models with random missing outputs is proposed. The distributions of missing outputs can be estimated in the VB-E step, and the distributions of unknown parameters can be estimated in the VB-M step by the estimated missing outputs and the available outputs. Compared with the expectation-maximization-based iterative algorithm, this algorithm computes the latent variable and the parameter distributions at each iteration. Therefore, it is more accurate. The simulation results demonstrate the advantages of the proposed algorithm.

关键词： Parameter estimation Missing outputs Variational Bayesian approach ARX model iterative algorithm

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