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Non-parametric Bayesian super-resolution

IET RADAR SONAR AND NAVIGATION 2010年第4期4卷 639-648页

作者： Lane, R. O. QinetiQ Malvern Technol Ctr Malvern WR14 3PS Worcs England

Super-resolution of signals and images can improve the automatic detection and recognition of objects of interest. However, the uncertainty associated with this process is not often taken into consideration. This is important because the processing of noisy signals can result in spurious estimates of the scene content. This study reviews a variety of super-resolution techniques and presents two non-parametric Bayesian super-resolution algorithms that not only take uncertainty into account, but also retain knowledge about the output uncertainty in the form of a full probability distribution. One of the two Bayesian techniques is based on an analytical calculation re-interpreted as super-resolution, and the other is a novel numerical algorithm. Although the algorithms are presented as stand-alone techniques for image analysis, such Bayesian super-resolution algorithms can increase automatic target recognition performance over standard super-resolution.

关键词： nonparametric Bayesian superresolution image analysis probability automatic object detection object recognition Computer vision and image processing techniques object detection numerical analysis probability distribution Image recognition signal superresolution numerical algorithm automatic object recognition Other numerical methods image superresolution image resolution Other topics in statistics

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An evaluation of algorithms for computing the covariance function of a multivariable arma process

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EUROPEAN JOURNAL OF CONTROL 2002年第4期8卷 315-325页

作者： Söderström, T Sebek, M Jezek, J Kucera, V Henrion, D Uppsala Univ Dept Syst & Control S-75103 Uppsala Sweden Acad Sci Czech Republ Inst Informat Theory & Automat CR-18208 Prague Czech Republic Czech Tech Univ Fac Elect Engn Ctr Appl Cybernet CZ-16627 Prague Czech Republic CNRS LAAS F-31077 Toulouse France

Computation of an ARMA covariance function is a common ingredient in analysis and synthesis of various problems in stochastic control, estimation and signal processing. In this paper, we present an algorithm based on simple polynomial calculations. Compared to alternative strategies, its computational load increases slowly with the order of the process. Further, it shows good numerical robustness and applies to multivariable ARMA processes, even with complex-valued coefficients.

关键词： covariance function ARMA process numerical algorithm numerical accuracy

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A Crank-Nicolson-type finite-difference scheme and its algorithm implementation for a nonlinear partial integro-differential equation arising from viscoelasticity

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COMPUTATIONAL & APPLIED MATHEMATICS 2020年第4期39卷 1-23页

作者： Zheng, Xuan Chen, Hongbin Qiu, Wenlin Cent South Univ Forestry & Technol Inst Math & Phys Coll Sci Changsha 410004 Hunan Peoples R China Hunan Normal Univ Key Lab Comp & Stochast Math Sch Math & Stat Minist Educ Changsha 410081 Hunan Peoples R China

A Crank-Nicolson-type finite-difference scheme is proposed and analyzed for a nonlinear partial integro-differential equation arising from viscoelasticity. The time derivative is approximated by the Crank-Nicolson scheme and the Riemann-Liouville fractional integral term is treated by means of the trapezoidal convolution quadrature rule. To construct a fully discrete difference scheme, the standard centered difference formula is utilized to approximate the second-order spatial derivative and the Galerkin method based on piecewise linear test functions is used to discrete the nonlinear convection term. Theoretical results of stability and convergence are derived using the non-negative character of the real quadratic form associated with the convolution quadrature, and combining with the discrete Gronwall inequality. Besides, a fixed point iterative numerical algorithm, which fills the gap that the existed numerical schemes have only theoretical analysis but no numerical results, is presented. numerical results show the efficiency and feasibility of our scheme, and the orders of convergence are in good agreement with the theoretical results.

关键词： Nonlinear partial integro-differential equation Crank-Nicolson-type finite-difference scheme Convolution quadrature Stability and convergence numerical algorithm numerical experiment

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Closed-Form Expressions for the Quantile Function of the Chi Square Distribution Using the Hybrid of Quantile Mechanics and Spline Interpolation

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WIRELESS PERSONAL COMMUNICATIONS 2020年第3期115卷 2093-2112页

作者： Okagbue, Hilary I. Adamu, Muminu O. Anake, Timothy A. Covenant Univ Dept Math Ota Nigeria Univ Lagos Dept Math Lagos Nigeria

Chi square distribution is a continuous probability distribution primarily used in hypothesis testing, contingency analysis, and construction of confidence limits in inferential statistics but not necessarily in the modeling of real-life phenomena. The closed-form expression for the quantile function (QF) of Chi square is not available because the cumulative distribution function cannot be transformed to yield the QF and consequently places limitations on the use of the QF. Researchers have over the years proposed approximations that improve over time in terms of speed, computational efficiency, and precision, and so on. However, most of the available closed-form expressions (quantile approximation) fail at the extreme tails of the distribution. This paper used the Quantile mechanics approach to obtain second-order nonlinear ordinary differential equations whose solutions using the power series method yielded initial approximates in form of series for different values of the degrees of freedom. The initial approximate varies with the exact (R software) values which serve as the reference and the error between them was minimized by the natural cubic spline interpolation. The final approximates are correct up to an average of 8 decimal places, have small error, and is closer to the exact when compared with some other results from other researchers. The upper tail of the distribution was considered and excellent results were obtained which is a major improvement over the existing results in the literature. The approach used in this work is a hybrid of series expansions and numerical algorithms. Computer codes can be written for the application.

关键词： Chi square Quantile function numerical algorithm Quantile mechanics Cubic spline Approximation

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Finding Optimal Solutions for Generalized Quantum State Discrimination Problems

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IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第12期63卷 7845-7856页

作者： Nakahira, Kenji Usuda, Tsuyoshi Sasaki Kato, Kentaro Hitachi Ltd Res & Dev Grp Yokohama Kanagawa 2440817 Japan Tamagawa Univ Quantum ICT Res Inst Quantum Informat Sci Res Ctr Machida Tokyo 1948610 Japan Aichi Prefectural Univ Sch Informat Sci & Technol Nagakute Aichi 4801198 Japan

We study an optimal quantum measurement for generalized quantum state discrimination problems, which include the problem of finding an optimal measurement maximizing the average success probability with and without a fixed rate of inconclusive results and the problem of finding an optimal measurement in the Neyman-Pearson strategy. We show that for any generalized quantum state discrimination problem, there is a corresponding minimum error discrimination problem sharing the same optimal measurement. We propose an approach in which the optimal measurement is obtained by solving the corresponding minimum error discrimination problem, and clarify the relationship between optimal solutions to the original and the corresponding problems, with which one can obtain an optimal solution to the original problem in some cases. Moreover, as an example of application of our approach, we present an algorithm for numerically obtaining optimal solutions to generalized quantum state discrimination problems.

关键词： Quantum state discrimination optimal measurements dual problems numerical algorithm

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Sector bounds in stability analysis and control design

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2020年第18期30卷 7857-7882页

作者： Xia, Meng Gahinet, Pascal Abroug, Neil Buhr, Craig Laroche, Edouard MathWorks Natick MA 01760 USA CEA LIST Gif Sur Yvette France Univ Strasbourg ICube Lab Illkirch Graffenstaden France

The sector stability theorem is an intuitive condition for the stability of feedback loops that unifies many lines of research including robust control and the theory of passive and dissipative systems. Applying this theorem typically requires checking or enforcing sector bounds on linear time-invariant systems. This article discusses practical and efficient numerical methods for performing these tasks. We derive a frequency-domain test for sector boundedness and use it to developO(n(3))numerical algorithms for computing the relative or directional indices of sector bounds. We also discuss how such algorithms can be combined with nonsmooth optimization techniques to enforce sector bounds while designing and tuning controllers. Several application examples illustrate the potential of these tools and techniques.

关键词： numerical algorithm passivity index sector bound

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Revisiting the method of characteristics via a convex hull algorithm

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JOURNAL OF COMPUTATIONAL PHYSICS 2015年 298卷 95-112页

作者： LeFloch, Philippe G. Mercier, Jean-Marc Univ Paris 06 Lab Jacques Louis Lions F-75252 Paris France Univ Paris 06 CNRS F-75252 Paris France CRIMERE F-75020 Paris France

We revisit the method of characteristics for shock wave solutions to nonlinear hyperbolic problems and we propose a novel numerical algorithm-the convex hull algorithm (CHA) which allows us to compute both entropy dissipative solutions (satisfying all entropy inequalities) and entropy conservative (or multi-valued) solutions. From the multi-valued solutions determined by the method of characteristics, our algorithm "extracts" the entropy dissipative solutions, even after the formation of shocks. It applies to both convex and non-convex flux/Hamiltonians. We demonstrate the relevance of the proposed method with a variety of numerical tests, including conservation laws in one or two spatial dimensions and problem arising in fluid dynamics. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Hyperbolic equations Method of characteristics numerical algorithm Compressible fluid

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On nonlinear fractional Klein-Gordon equation

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SIGNAL PROCESSING 2011年第3期91卷 446-451页

作者： Golmankhaneh, Alireza K. Golmankhaneh, Ali K. Baleanu, Dumitru Univ Pune Dept Phys Pune 411007 Maharashtra India Islamic Azad Univ Dept Phys Urmia Branch Oromiyeh Iran Islamic Azad Univ Dept Phys Mahabad Branch Mahabad Iran Cankaya Univ Dept Math & Comp Sci TR-06530 Ankara Turkey Inst Space Sci Magurele 76900 Romania

numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Cordon equation can be used as numerical algorithm. The behavior of solutions and the effects of different values of fractional order a are shown graphically. Some examples are given to show ability of the method for solving the fractional nonlinear equation. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.

关键词： Caputo fractional derivative Fractional Klein Gordon Homotopy perturbation method numerical algorithm Iteration method

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Cost minimization of real-time mission for software systems with rejuvenation

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2020年 193卷 106593-000页

作者： Levitin, Gregory Xing, Liudong Xiang, Yanping Univ Elect Sci & Technol China Sch Comp Sci Collaborat Auton Comp Lab Chengdu Sichuan Peoples R China Israel Elect Corp Ltd POB 10 IL-31000 Haifa Israel Univ Elect Sci & Technol China Sch Mech & Elect Engn Chengdu Sichuan Peoples R China Univ Massachusetts Dartmouth MA 02747 USA

This paper considers the optimal rejuvenation policy problem for software systems performing real-time tasks. Due to software aging, the system performance deteriorates with time eventually leading to the system crash, which can be catastrophic for critical applications. To prevent the system crash or minimize its occurrence probability, software rejuvenation has been widely adopted for counteracting the software aging effect but at the cost of extra system overhead and downtime. We derive the optimal state-based rejuvenation policy minimizing the total expected mission cost for software aging systems subject to multiple performance degradation states. The solution encompasses an event transition-based numerical method that assesses the total expected mission cost of a real-time task, covering penalty cost from the mission failure, operation cost of running the mission software and the expected rejuvenation cost. The proposed cost evaluation model can accommodate arbitrary types of state transition time distributions. The suggested model also allows simultaneous evaluations of other system performance metrics including the probability of the successful task completion (i.e., mission reliability) and conditional expected mission completion time given a successful mission task. Examples are presented to demonstrate the proposed methodology and optimizations. Effects of different parameters on the rejuvenation optimization solution are also investigated.

关键词： Event transition Mission cost Mission reliability Optimization Real-time task Software aging Software rejuvenation numerical algorithm

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Analysis of control for a free boundary problem of steady plaques in the artery

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APPLIED MATHEMATICS AND COMPUTATION 2018年 331卷 473-483页

作者： Miniak-Gorecka, Alicja Nowakowski, Andrzej Univ Lodz Lodz Poland

In the earlier paper of Friedman et al. a simplified model of plaque growth involving LDL and HDL cholesterols, macrophages and foam cells is considered and they satisfy a coupled system of PDEs with a free boundary. The paper adds some control function to that model, allowing the controlled growth of LDL, HDL and plaque. Next, the new dual dynamic programming approach for free boundary problem is developed to formulate sufficient optimality conditions for the optimal steering of drugs. Finally an approximate optimality and numerical calculations are presented. (C) 2018 Published by Elsevier Inc.

关键词： Atherosclerosis Optimal control numerical algorithm

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