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Total Least-Squares Estimation for 2D Affine Coordinate Transformation with Constraints on Physical Parameters

JOURNAL OF SURVEYING ENGINEERING 2016年第3期142卷 04016009-1-04016009-5页

作者： Zhang, Songlin Zhang, Kun Liu, Pengcheng Tongji Univ Coll Surveying & Geoinformat Shanghai 200092 Peoples R China East China Normal Univ Lab Geog Informat Sci Shanghai 200062 Peoples R China Cent China Normal Univ Coll Urban & Environm Sci Wuhan 430079 Peoples R China

The error-in-variable (EIV) model takes the error of all variables into account and has been widely applied to many practical problems arising in environmental study, geology, geographic information science (GIS), and geodesy. Coordinate transformations are among the most frequently encountered problems in spatial data processing, and the EIV model can be built based on two sets of coordinates. In some applications, physical parameterssuch as the shift, rotation angle, and scale factorhave constraints. Current implementations of the constrained EIV (CEIV) model do not consider physical constraints explicitly. The purpose of this paper is to convert physical constraints into mathematical forms and to use constrained total least squares (CTLS) to solve the CEIV problem of two-dimensional (2D) affine transformation. The effectiveness of this method is illustrated through a numerical example.

关键词： CEIV model 2D affine transformation Constraints iterative algorithm

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iterative algorithms for improving consistency of intuitionistic preference relations

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2014年第5期65卷 708-722页

作者： Xu, Z. Xia, M. PLA Univ Sci & Technol Nanjing 210007 Jiangsu Peoples R China Tsinghua Univ Beijing 100084 Peoples R China

Consistency of preference relations is an important research topic in decision making with preference information. The existing research about consistency mainly focuses on multiplicative preference relations, fuzzy preference relations and linguistic preference relations. Intuitionistic preference relations, each of their elements is composed of a membership degree, a non-membership degree and a hesitation degree, can better reflect the very imprecision of preferences of decision makers. There has been little research on consistency of intuitionistic preference relations up to now, and thus, it is necessary to pay attention to this issue. In this paper, we first propose an approach to constructing the consistent (or approximate consistent) intuitionistic preference relation from any intuitionistic preference relation. Then we develop a convergent iterative algorithm to improve the consistency of an intuitionistic preference relation. Moreover, we investigate the consistency of intuitionistic preference relations in group decision making situations, and show that if all individual intuitionistic preference relations are consistent, then the collective intuitionistic preference relation is also consistent. Moreover, we develop a convergent iterative algorithm to improve the consistency of all individual intuitionistic preference relations. The practicability and effectiveness of the developed algorithms is verified through two examples.

关键词： group decision making intuitionistic preference relation consistency iterative algorithm

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Combination of voxel-based and projection-based methods in terms of convergence for CT reconstruction

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MEDICAL PHYSICS 2016年第6期43卷 2828-2834页

作者： Chukanov, Viacheslav Bergner, Frank SPbPU St Petersburg 195251 Russia Philips GmbH Res Labs D-22335 Hamburg Germany

Purpose: Recent applications of iterative image reconstruction algorithms to multislice helical CT have shown that iterative reconstruction can significantly improve image quality and reduce artifacts. In this paper, the authors introduce a combination of two different algorithms with different convergence properties: ordered subsets separable paraboloidal surrogates (OS-SPS) and iterative coordinate descent (ICD). The first one updates image voxels simultaneously, slightly changing attenuation values iteration by iteration. The second algorithm updates image voxel by voxel, each time performing full forward and backward projections of the voxel. It has been shown that ICD converges better at high-frequency areas and requires more iterations to reconstruct low-frequency components of the image. In contrast to ICD, SPS requires multiple iterations to reconstruct high-frequency areas. In this paper, the authors introduce an algorithm which leverages the benefits of both ICD and SPS. Methods: The idea is to update the entire image with SPS, determine high-frequency components, and focus ICD computations on it using nonhomogeneous ICD update. Results: The authors have successfully implemented OS-SPS, ICD, their hybrid approach, and few variations of ICD based on spatially nonuniform updates. Conclusions: The authors have examined the convergence of different algorithms and found that proposed algorithm converges better than OS-SPS, ICD, as well as various improved variants of ICD. (C) 2016 American Association of Physicists in Medicine.

关键词： computed tomography iterative algorithm coordinate descent separable paraboloidal surrogate ordered subsets

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Optimization-based image reconstruction with artifact reduction in C-arm CBCT

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PHYSICS IN MEDICINE AND BIOLOGY 2016年第20期61卷 7300-7333页

作者： Xia, Dan Langan, David A. Solomon, Stephen B. Zhang, Zheng Chen, Buxin Lai, Hao Sidky, Emil Y. Pan, Xiaochuan Univ Chicago Dept Radiol Chicago IL 60637 USA GE Global Res Niskayuna NY USA Mem Sloan Kettering Canc Ctr 1275 York Ave New York NY 10021 USA Univ Chicago Dept Radiat & Cellular Oncol Chicago IL 60637 USA

We investigate an optimization-based reconstruction, with an emphasis on image-artifact reduction, from data collected in C-arm cone-beam computed tomography (CBCT) employed in image-guided interventional procedures. In the study, an image to be reconstructed is formulated as a solution to a convex optimization program in which a weighted data divergence is minimized subject to a constraint on the image total variation (TV);a data-derivative fidelity is introduced in the program specifically for effectively suppressing dominant, low-frequency data artifact caused by, e.g. data truncation;and the Chambolle-Pock (CP) algorithm is tailored to reconstruct an image through solving the program. Like any other reconstructions, the optimization-based reconstruction considered depends upon numerous parameters. We elucidate the parameters, illustrate their determination, and demonstrate their impact on the reconstruction. The optimization-based reconstruction, when applied to data collected from swine and patient subjects, yields images with visibly reduced artifacts in contrast to the reference reconstruction, and it also appears to exhibit a high degree of robustness against distinctively different anatomies of imaged subjects and scanning conditions of clinical significance. Knowledge and insights gained in the study may be exploited for aiding in the design of practical reconstructions of truly clinical-application utility.

关键词： cone-beam CT C-arm optimization-based reconstruction iterative algorithm data truncation

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An iterative method for robust in-line phase contrast imaging

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NEW JOURNAL OF PHYSICS 2016年第4期18卷 043003-043003页

作者： Carroll, Aidan J. van Riessen, Grant A. Balaur, Eugeniu Dolbnya, Igor P. Tran, Giang N. Peele, Andrew G. La Trobe Univ La Trobe Inst Mol Sci Dept Chem & Phys Bundoora Vic 3086 Australia ARC Ctr Excellence Adv Mol Imaging Canberra ACT Australia Diamond Light Source Ltd Harwell Sci & Innovat Campus Didcot OX11 ODE Oxon England Australian Synchrotron 800 Blackburn Rd Clayton Vic 3168 Australia

We present an iterative near-field in-line phase contrast method that allows quantitative determination of the thickness of an object given the refractive index of the sample material. The iterative method allows for quantitative phase contrast imaging in regimes where the contrast transfer function (CTF) and transport of intensity equation (TIE) cannot be applied. Further, the nature of the iterative scheme offers more flexibility and potentially allows more high-resolution image reconstructions when compared to TIE method and less artefacts when compared to the CTF method. While, not addressed here, extension of our approach in future work to broadband illumination will also be straightforward as the wavelength dependence of the refractive index of an object can be readily incorporated into the iterative approach.

关键词： x-ray microscope iterative algorithm near field phase contrast imaging

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An iterative algorithm for Solving a System of Nonlinear Algebraic Equations, F(x)=0, Using the System of ODEs with an Optimum α in (x) over dot = λ[αF + (1-a)B^TF];B_ij = partial derivativeF_i/partial derivativex_j

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CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES 2011年第4期73卷 395-431页

作者： Liu, Chein-Shan Atluri, Satya N. Natl Taiwan Univ Dept Civil Engn Taipei 10764 Taiwan Univ Calif Irvine Ctr Aerosp Res & Educ Irvine CA USA

In this paper we solve a system of nonlinear algebraic equations (NAEs) of a vector-form: F(x) = 0. Based-on an invariant manifold defined in the space of (x, t) in terms of the residual-norm of the vector F(x), we derive a system of nonlinear ordinary differential equations (ODEs) with a fictitious time-like variable t as an independent variable: (x) over dot = lambda[alpha F + (1 - alpha)(BF)-F-T], where lambda and alpha are scalars and B-ij = partial derivative F-i/partial derivative x(j). From this set of nonlinear ODEs, we derive a purely iterative algorithm for finding the solution vector x, without having to invert the Jacobian (tangent stiffness matrix) B. Here, we introduce three new concepts of attracting set, bifurcation and optimal combination, which are controlled by two parameters gamma and alpha. Because we have derived all the related quantities explicitly in terms of F and its differentials, the attracting set, and an optimal alpha can be derived exactly. When gamma changes from zero to a positive value the present algorithms undergo a Hopf bifurcation, such that the convergence speed is much faster than that by using gamma = 0. Moreover, when the optimal alpha is used we can further accelerate the convergence speed several times. Some numerical examples are used to validate the performance of the present algorithms, which reveal a very fast convergence rate in finding the solution, and which display great efficiencies and accuracies than achieved before.

关键词： Nonlinear algebraic equations Non-Linear Ordinary Differential Equations Non-Linear Partial Differential Equations Optimal Vector Driven algorithm (OVDA) iterative algorithm Attracting set Hopf bifurcation Intermittency Jordan algebra

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一类具有非线性边界条件的四阶方程的紧差分迭代解法

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高等学校计算数学学报 2016年第4期38卷 289-300页

作者：庄清渠任全伟华侨大学数学科学学院上海师范大学数理学院

1引言科学和工程计算中许多问题的数学模型都可用四阶微分方程来表述.如刻画火焰传播的Kuramoto-Sivashinsky方程以及描述固体复杂的相位分离以及粗化现象的CahnHilliard方程[1,2,3].而在应用惩罚法于带有边界约束的四阶变分不等式时则... 详细信息

1引言科学和工程计算中许多问题的数学模型都可用四阶微分方程来表述.如刻画火焰传播的Kuramoto-Sivashinsky方程以及描述固体复杂的相位分离以及粗化现象的CahnHilliard方程[1,2,3].而在应用惩罚法于带有边界约束的四阶变分不等式时则会产生带非线性边界条件的四阶方程[4].本文的目的是考虑如下四阶非线性边值问题

关键词： Fourth-order differential equation Nonlinear boundary condition Compact difference scheme iterative algorithm

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A Modified Magnetic Gradient Contraction Based Method for Ferromagnetic Target Localization

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SENSORS 2016年第12期16卷 2168-2168页

作者： Wang, Chen Zhang, Xiaojuan Qu, Xiaodong Pan, Xiao Fang, Guangyou Chen, Luzhao Chinese Acad Sci Key Lab Electromagnet Radiat & Sensing Technol Beijing 100190 Peoples R China Univ Chinese Acad Sci Beijing 100039 Peoples R China

The Scalar Triangulation and Ranging (STAR) method, which is based upon the unique properties of magnetic gradient contraction, is a high real-time ferromagnetic target localization method. Only one measurement point is required in the STAR method and it is not sensitive to changes in sensing platform orientation. However, the localization accuracy of the method is limited by the asphericity errors and the inaccurate value of position leads to larger errors in the estimation of magnetic moment. To improve the localization accuracy, a modified STAR method is proposed. In the proposed method, the asphericity errors of the traditional STAR method are compensated with an iterative algorithm. The proposed method has a fast convergence rate which meets the requirement of high real-time localization. Simulations and field experiments have been done to evaluate the performance of the proposed method. The results indicate that target parameters estimated by the modified STAR method are more accurate than the traditional STAR method.

关键词： ferromagnetic target localization magnetic gradient tensor magnetic dipole iterative algorithm

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A new iteration process for approximation of fixed points of mean nonexpansive mappings in CAT(0) spaces

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COGENT MATHEMATICS 2017年第1期4卷 0-0页

作者： Abkar, A. Rastgoo, M. Imam Khomeini Int Univ Dept Math Qazvin 34149 Iran

In this paper, we introduce a new iterative algorithm for approximating fixed points of mean nonexpansive mappings in CAT(0) spaces. We prove a Delta-convergence theorem under suitable conditions. The result we obtain improves and extends several recent results stated by many others;they also complement many known recent results in the literature. We then provide some numerical examples to illustrate our main result and to display the efficiency of the proposed algorithm.

关键词： CAT(0) space mean nonexpansive mapping Delta-convergence iterative algorithm fixed point

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Spectrum Allocation Scheme Based on Stackelberg Game in Two-tier HetNet

Spectrum Allocation Scheme Based on Stackelberg Game in Two-...

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2016 IEEE 13th International Conference on Signal Processing（ICSP2016）

作者： Jing Dai Wei Lv Fang Ye College of Information and Communication Engineering Harbin Engineering University China United Network Communications Limited Heilongjiang Branch

As the explosive growth of wireless date requirements, heterogeneous network(HetN et) has become an effective solution for improving the system performance such as the throughput. The femtocells are always arranged to share the spectrum with the macro base stations(MBSs). Thus, the cochannel interference leads to the degradation of the HetN et throughput. In this paper, we discuss the program of spectrum reuse in the two-tier Het Net, and the problem is defined as a Stackelberg game approach. The MBS is play as a leader and it releases a part of spectrum resource for femtocells to avoid intertier interference. And the femtocells provide services to fractional macro users(MUEs) in return. Therefore, the throughput can be improved by the reduction of the inter-tier interference. Compared with the former works, the prominent characteristic of the method in the paper is that the benefit relation between the leader and followers is not measured by the real money. Furthermore, considering the system throughput specifically, we define the utility of the femto base stations(FBSs) by the average throughput as same as the utility of the MBS, which is used to improve the overall throughput of the system. Moreover, the gradient descent algorithm is also applied to compute the Nash equilibrium as the range of variables become continuous. The simulation results indicate that the proposed algorithm can observably reduce the interference and enhance the throughput of the network.

关键词： Stackelberg Game Het Net spectrum reuse iterative algorithm

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