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A fast regularized iterative algorithm for fan-beam CT reconstruction

PHYSICS IN MEDICINE AND BIOLOGY 2019年第14期64卷 145006-145006页

作者： Wang, Ting Kudo, Hiroyuki Yamazaki, Fukashi Liu, Huafeng Zhejiang Univ State Key Lab Modern Opt Instrumentat Hangzhou 310027 Zhejiang Peoples R China Univ Tsukuba Fac Engn Informat & Syst Tennoudai 1-1-1 Tsukuba Ibaraki 3058573 Japan

We propose a fast iterative image reconstruction algorithm for normal, short-scan, and super-shortscan fan-beam computed tomography (CT), which aims at iterative reconstruction for low-dose and few-view CT by minimizing a data-fidelity term regularized with a total variation (TV) penalty. The derivation of the algorithm can be outlined as follows. First, the original minimization problem is formulated into a saddle-point (primal-dual) problem by using the Lagrangian duality, to which we apply the alternating projection proximal (APP) algorithm, which belongs to a class of first-order primal-dual methods. Second, we precondition the iterative formula using the modified ramp filter of the filtered back-projection (FBP) reconstruction algorithm in such a way that the solution to this preconditioned iteration perfectly coincides with the solution to the original problem. The resulting algorithm converges quickly to the minimizer of the cost function. To demonstrate the advantages of our method, we perform reconstruction experiments using projection data from both numerical phantoms and real CT data. Both qualitative and quantitative results are presented.

关键词： fan-beam CT short-scan image reconstruction iterative algorithm total variation

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A NEW iterative algorithm FOR SOLVING A SYSTEM OF GENERALIZED EQUILIBRIUM PROBLEMS

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS

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JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS 2018年 2018卷

作者： Abkar, A. Shekarbaigi, M. Aghamohammadi, N. Imam Khomeini Int Univ Dept Pure Math Fac Sci Qazvin 34149 Iran

In this paper, under the framework of real Hilbert spaces, we introduce a new iterative algorithm for finding a common element in the solution set of a generalized equilibrium problem and in the fixed-point sets of a family of nonexpansive mappings. We obtain strong convergence theorems of the common solution problem. An example is provided to support the convergence analysis.

关键词： iterative algorithm Generalized equilibrium problem Variational inequality Nonexpansive mapping Strongly monotone operator

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An iterative algorithm Based on the Dual Integral Inversion for Particle Sizing

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2018年第7期67卷 1729-1737页

作者： Niu, He Cao, Zhang Xie, Heng Zhang, Jiawen Xu, Lijun Beihang Univ Sch Instrument Sci & Optoelect Engn Dept Measurement & Control Beijing 100191 Peoples R China Beijing Adv Innovat Ctr Big Data Based Precis Med Beijing 100191 Peoples R China Beihang Univ Minist Educ Key Lab Precis Optomechatron Technol Beijing 100191 Peoples R China

In this paper, an iterative algorithm is proposed to retrieve the particle-size distributions via Fraunhofer diffraction. A dual integral inversion was proposed in our previous work, the inversion is robust and generates precise particle sizing, if the diffraction pattern can be accurately captured. In real applications, the pattern can only be partially detected, and the inversion fails to reconstruct the size distributions in detail. However, the results of the inversion can be used to produce an initial estimate. Then, a simulated diffraction pattern was generated from the estimated particle sizes. The deviation between the measured pattern and the simulated one was deduced to correct the results of particle sizing. The corrections can be achieved in an iterative approach, and the particle-size distribution was updated subsequently. The iteration stopped once the deviation was below the target value. Both simulation and experiment were conducted to validate the feasibility and effectiveness of the proposed algorithm. The results demonstrate that the size distribution from the proposed algorithm agrees well with the original phantoms for both noise-free and noise-contaminated data.

关键词： Fraunhofer diffraction integral inversion iterative algorithm laser scattering particle sizing

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iterative Tree algorithm to Evaluate Terahertz Signal Contribution of Specific Optical Paths Within Multilayered Materials

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IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY 2019年第6期9卷 684-694页

作者： Cassar, Quentin Chopard, Adrien Fauquet, Frederic Guillet, Jean-Paul Pan, Mingming Perraud, Jean-Baptiste Mounaix, Patrick Univ Bordeaux UMR CNRS 5218 IMS Lab F-33400 Talence France

Terahertz time-domain spectroscopy is a specifically appropriated technique to analyze layered structure composition and dimension. Inverse electromagnetic problems are commonly solved to extract, from a recorded terahertz-signal, the distinctive layer dielectric properties and thicknesses. However, main origins and formation routes of the signal are left unassessed while it could be of great value to deepen and to enlarge stratified material terahertz-probing property knowledge and understanding. In this article, a new numerical method to reconstruct and to analyze terahertz experimental signals is reported. It consists of an iterative algorithm implementing a connected propagation tree where each node of the tree denotes the occurrence of the incident pulse division. Descendent pulses are individually monitored and their carried proportion of the incident power can be evaluated. Therefore, it provides a flowchart of the predominant optical paths contributing to the structure response. On this basis, a simplified global transfer function is automatically derived by the algorithm. The effectiveness of the numerical procedure is demonstrated through the reconstruction and the analysis of a reflected terahertz-signal from an aerospace coating structure with individual and different thicknesses of several tens of microns. The recovered signal is first discussed as a function of the sum of pulses detected at each iteration. Then, the power proportion distribution for each iteration is studied to delimit the meaningful number of required algorithm iteration. Finally, within each iteration are sorted the most contributing optical paths and a simplified global transfer function is derived. The present algorithm allowed to identify the main propagations inside this stratified material giving arise to the recorded signal and to reduce by ${\text{98.23}}\%$ the number of considered and calculated optical paths compared to the standard signal reconstruction procedure.

关键词： iterative algorithms iterative algorithm optical path analysis stratified materials terahertz signal reconstruction

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An iterative algorithm for Dual-Frequency Signals With Unknown Frequencies and Amplitudes 10

An Iterative Algorithm for Dual-Frequency Signals With Unkno...

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10th International Conference on Modelling, Identification and Control (ICMIC)

作者： Liu, Siyu Song, Guanglei Ding, Feng Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Jiangsu Peoples R China Wuxi Inst Technol Sch Mech Technol Wuxi 214121 Jiangsu Peoples R China

ISBN: (纸本)9781538654163

A new iterative parameter estimation algorithm is proposed to estimate all parameters of dual-frequency signals including the unknown amplitudes, frequencies and phases. The observation data of the signals are disturbed by stochastic noise. The key is that the signal model is a highly nonlinear function in regard to the frequencies and phases. A gradient based iterative algorithm is presented to compare the algorithm performance. The performance of the proposed method is tested by simulation.

关键词： Parameter estimation Signal model Gradient search Newton method iterative algorithm

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Auxiliary Principle and iterative algorithm for a Generalized Nonlinear Mixed Quasi-variational-like Inequality

Auxiliary Principle and Iterative Algorithm for a Generalize...

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2019 International Conference on Applied Mathematics, Modeling, Simulation and Optimization(AMMSO 2019)

作者： Ya-li ZHAO Xin LIU Dong-xue HAN College of physics and Mathematics Bohai University

In this paper, we employ the auxiliary principle technique to study a generalized nonlinear mixed quasi-variational-like inequality in Hilbert spaces. Fist, we establish the existence and uniqueness of solution of the corresponding auxiliary generalized nonlinear mixed quasi-variational-like inequality by making use of minimizing sequence of a convex function. Then based on the existence result, we construct an iterative algorithm for finding approximate solution to the exact solution of the generalized nonlinear mixed quasi-variational-like inequality. Our results extend, improve and unify some known results in the literature.

关键词： Generalized nonlinear mixed quasi-variational-like inequality Auxiliary principle technique Minimizing sequence iterative algorithm Convergence

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A Data Driven Empirical iterative algorithm for GSR Signal Pre-Processing 26

A Data Driven Empirical Iterative Algorithm for GSR Signal P...

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European Signal Processing Conference (EUSIPCO)

作者： Gautam, Arvind Simoes-Capela, Neide Schiavone, Giuseppina Acharyya, Amit de Raedt, Walter Van Hoof, Chris IMEC Kapeldreef 75 Heverlee Belgium Indian Inst Technol Hyderabad Elect Engn Dept Sangareddy India Katholieke Univ Leuven Elect Engn Dept ESAT Kasteelpk Arenberg 10 Heverlee Belgium IMEC NL High Tech Campus 31 Eindhoven Netherlands

ISBN: (纸本)9789082797015

In this paper, we introduce a data driven iterative low pass filtering technique, the Empirical iterative algorithm (EIA) for Galvanic Skin Response (GSR) signal preprocessing. This algorithm is inspired on Empirical Mode Decomposition (EMD), with performance enhancements provided by applying Midpoint-based Empirical Decomposition (MED), and removing the sifting process in order to make it computational inexpensive while maintaining effectiveness towards removal of high frequency artefacts. Based on GSR signals recorded at the wrist we present an algorithm benchmark, with results from EIA being compared with a smoothing technique based on moving average filter commonly used to pre-process GSR signals. The comparison is established on data from 20 subjects, collected while performing 33 different randomized activities with right hand, left hand and both hands, respectively. In average, the proposed algorithm enhances the signal quality by 51%, while the traditional moving average filter reaches 16% enhancement. Also, it performs 136 times faster than the EMD in terms of average computational time. As a show case, using the GSR signal from one subject, we inspect the impact of applying our algorithm on GSR features with psychophysiological relevance. Comparison with no preprocessing and moving average filtering shows the ability of our algorithm to retain relevant low frequency information.

关键词： EMD Data driven iterative algorithm GSR EDA Skin conductance

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

Convergence Characterization of an Iterative Algorithm for C...

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第三十八届中国控制会议

作者： Shun-Qiang You Ying Zhang Ai-Guo Wu Harbin Institute of Technology

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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An iterative algorithm with a Tuning Parameter for Continuous Lyapunov Matrix Equations 37

An Iterative Algorithm with a Tuning Parameter for Continuou...

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37th Chinese Control Conference (CCC)

作者： Wang, Zhi-Qun Sun, Hui-Jie Wu, Ai-Guo Chai, Hua Harbin Inst Technol Shenzhen Grad Sch Shenzhen 518055 Peoples R China CNPC Nat Gas Plant ChangQing Oil Field Constituent Co Jingbian 718500 Shaanxi Peoples R China

ISBN: (纸本)9789881563958

In this paper, by introducing a tuning parameter, an explicit iterative algorithm is constructed for solving the continuous Lyapunov matrix equations associated with Ito stochastic systems. A necessary and sufficient condition is provided to guarantee the convergence of the proposed algorithm by using the Kronecker product. Moreover, some easily verifiable convergence results are developed for the proposed algorithm based on the obtained necessary and sufficient condition. In addition, a method is given for the selection of the optimal tuning parameter. Finally, an example is applied to verify the effectiveness of the presented algorithm.

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

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An iterative algorithm for solving sparse linear equations

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2017年第7期46卷 5113-5122页

作者： Walker, Stephen G. Univ Texas Austin Dept Math Austin TX 78712 USA

This article introduces a new iterative technique for solving systems of linear equations of the kind Ax = b. Convergence, and with a given rate, is guaranteed with the square nonsingular matrix A being non-negative. The iterative algorithm depends on a scheme derived from Bayesian updating. The algorithm is shown to compare very favorably with the wisely used GMRES routine. With the algorithm being easy to code, it has the potential to be highly useable.

关键词： Bayesian update iterative algorithm Non-negative matrix Stochastic matrix

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