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American Control Conference (ACC)

作者： R. Pytlak T. Tarnawski Faculty of Cybernetics Military University of Technology Warsaw Poland

The paper describes new limited memory quasi-Newton algorithms for large scale nonconvex problems with box constraints. The algorithms employ a direction of descent obtained by applying limited memory quasi-Newton updates. In order to cope with box constraints a projection operator on a feasible set is applied. We introduce several algorithms which mainly differ by a directional minimization rule. We show that for the considered line search rules, under the assumption that the objective function is strictly convex, the limited memory BFGS versions are globally convergent. Furthermore, we are able to show that after a finite number of iterations the methods identify an active set at a solution. We believe that the proposed algorithms are competitive to L-BFGS-B algorithm. We give some numerical results which support our claim.

关键词： Cybernetics Paper technology Convergence projection algorithms Cities and towns Large-scale systems Minimization methods Newton method Algorithm design and analysis Constraint theory

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On Utility-Based Power Control and Receive Beamforming

On Utility-Based Power Control and Receive Beamforming

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Annual Conference on Information Sciences and Systems (CISS)

作者： Slawomir Stanczak Angela Feistel Daniel Tomecki Fraunhofer German-Sino Laboratory for Mobile Communications MCI Berlin Germany Heinrich-Hertz-Chair for Mobile Communications Technical University Berlin Berlin Germany

The paper deals with the problem of joint power control and receive beamforming in wireless networks. The objective is to allocate transmit powers and receive beamformers to the users in order to maximize a weighted sum of some utility functions of the signal-to-interference ratios. We propose using a class of utility functions with increasing relative concavity that allows for an arbitrarily close approximation of the max-min fair rate allocation. Then, we consider a gradient projection algorithm for the problem, show its local convergence and address the problem of implementing it in a distributed manner.

关键词： Power control Array signal processing Mobile communication Wireless networks projection algorithms Convergence Resource management Interference Throughput Aggregates

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Online Sparse Kernel-Based Classification by projections

Online Sparse Kernel-Based Classification by Projections

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IEEE Workshop on Machine Learning for Signal Processing

作者： Konstantinos Slavakis Sergios Theodoridis Isao Yamada Department of Informatics and Telecommunications University of Athens (NKUA) Athens Greece Department of Communications and Integrated Systems Tokyo Institute of Technology Tokyo Japan

This paper presents a novel sparse approximation method for online classification in Reproducing Kernel Hilbert Spaces (RKHS) by exploiting adaptive projection-based algorithms. We use convex analysis to revisit the standard kernel-based classification task as the problem of finding a point that belongs to a closed halfspace (a special closed convex set) in an RKHS. In such a way, classification in an online setting, where data arrive sequentially, is treated as the task of finding a point in the nonempty intersection of an infinite sequence of closed halfspaces in RKHS. Convex analysis is also used to introduce sparsification arguments in the design by imposing a simple convex constraint on the norm of the classifier. An algorithmic solution to this optimization problem, where new convex constraints are added every time instant, is given by the recently introduced Adaptive Projected Subgradient Method (APSM) which unifies a number of well-known adaptive projection-based algorithms such as the classical Normalized Least Mean Squares (NLMS) and the Affine projection Algorithm (APA). Several theoretical results are established for the generated sequence of classifiers in the RKHS: monotone approximation, strong convergence, asymptotic optimality, and characterization of the limit classifier. Further, we show that the additional convex constraint on the norm of the classifier naturally leads to an online sparse approximation of the resulting kernel series expansion. The validation of the proposed method is performed by considering the adaptive equalization of a nonlinear communication channel.

关键词： Kernel Least squares approximation Approximation methods Hilbert space Approximation algorithms Constraint optimization projection algorithms Character generation Convergence Adaptive equalizers

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Fast Photoacoustic Imaging System Based on Multi-element Linear Transducer Array CT-scanning

Fast Photoacoustic Imaging System Based on Multi-element Lin...

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2007 IEEE/ICME International Conference on Complex Medical Engineering-CME2007(CME2007 第二届国际复合医学工程学术大会)

作者： Diwu Yang Da Xing Sihua Yang Liangzhong Xiang Lvming Zeng MOE Key Laboratory of Laser Life Science & Institute of Laser Life Science South China Normal University Guangzhou 510631 China

In this paper, a new photoacoustic imaging system based on multi-element linear transducer array CT-scanning was present. In this imaging system, the 532-nm laser light with the repetition rate of 10 Hz and the pulse width of 10 ns used as the excitation source. A 64-element linear transducer array with the central frequency of 7.5MHz is used to capture photoacoustic signals by rotating the multi-element linear transducer array with a step of 18 degrees. The photoacoustic images are reconstructed by the modified limited-field filtered back projection algorithm, which is modified from the limited-field filtered back projection algorithm adapt to reconstruct the photoacoustic images with the photoacoustic signals collected by CT-scanning. The experiments of a phantom model and in vitro blood vessels were performed with this system. A clear image can be obtained within 1 minute. The experimental results demonstrate the reconstructed photoacoustic images with this system are greatly improved;the boundaries of the round absorbers and almost the vascular ramifications of the chick embryo chorioallantoic membrane are accurately resolved. This system may have potential in clinical application to fast image the protrudent organs of the human body, such as breast and head.

关键词： Transducers Image reconstruction projection algorithms Optical pulses Space vector pulse width modulation Laser excitation Frequency Imaging phantoms In vitro Blood vessels

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Convergence rate analysis and error bounds for projection algorithms in convex feasibility problems

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OPTIMIZATION METHODS & SOFTWARE 2003年第4期18卷 377-394页

作者： Beck, A Teboulle, M Tel Aviv Univ Sch Math Sci IL-69978 Tel Aviv Israel

We analyze the rate of convergence of three basic projections type algorithms for solving the convex feasibility problem (CFP). Error bounds are known to be central in establishing the rate of convergence of iterative methods. We study the interplay between Slater's hypothesis on CFP and a specific local error bound (LEB). We show that without Slater's hypothesis on CFP, projections type algorithms can in fact behave quite badly, i.e., with a rate of convergence which is not bounded. We derive a new and simple convex analytic proof showing that Slater's hypothesis on CFP implies LEB and hence linear convergence of projection algorithms is guaranteed. We then propose an alternative local error bound derived from the gradient projection algorithm for convex minimization which is proven to be weaker than LEB and used to derive further convergence rate results.

关键词： convex feasibility projection algorithms error bounds convergence rate convex minimization

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Membership set identification with periodic inputs and orthonormal regressors

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SIGNAL PROCESSING 2006年第12期86卷 3778-3786页

作者： Akcay, Huseyin At, Nuray Anadolu Univ Dept Elect & Elect Engn TR-26470 Eskisehir Turkey

In this paper, we study the central and the projection algorithms in membership-set estimation with periodic input signals and orthonormal basis functions for the special case that the number of the estimated parameters equals the input period (or overparameterized model structures). First, we derive explicit formulae for a central algorithm and the diameter of the membership set. Then, we characterize the set of all projection algorithms. (c) 2006 Elsevier B.V. All rights reserved.

关键词： identification membership set orthonormal basis functions periodic inputs central algorithms projection algorithms

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Linearly constrained global optimization and stochastic differential equations

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JOURNAL OF GLOBAL OPTIMIZATION 2006年第2期36卷 191-217页

作者： Parpas, Panos Rustem, Berc Pistikopoulos, Efstratios N. Univ London Imperial Coll Sci Technol & Med Dept Comp London SW7 2AZ England Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2AZ England

A stochastic algorithm is proposed for the global optimization of nonconvex functions subject to linear constraints. Our method follows the trajectory of an appropriately defined Stochastic Differential Equation (SDE). The feasible set is assumed to be comprised of linear equality constraints, and possibly box constraints. Feasibility of the trajectory is achieved by projecting its dynamics onto the set defined by the linear equality constraints. A barrier term is used for the purpose of forcing the trajectory to stay within the box constraints. Using Laplace's method we give a characterization of a probability measure (Pi) that is defined on the set of global minima of the problem. We then study the transition density associated with the projected diffusion process and show that its weak limit is given by Pi. Numerical experiments using standard test problems from the literature are reported. Our results suggest that the method is robust and applicable to large-scale problems.

关键词： stochastic global optimization simulated annealing stochastic differential equations Fokker-Planck equation Laplace's method projection algorithms

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Distributed kernel regression: An algorithm for training collaboratively

Distributed kernel regression: An algorithm for training col...

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IEEE Information Theory Workshop

作者： Predd, J. B. Kulkarni, S. R. Poor, H. V. Princeton Univ Dept Elect Engn Princeton NJ 08540 USA

ISBN: (纸本)9781424400355

This paper addresses the problem of distributed learning under communication constraints, motivated by distributed signal processing in wireless sensor networks and data mining with distributed databases. After formalizing a general model for distributed learning, an algorithm for collaboratively training regularized kernel least-squares regression estimators is derived. Noting that the algorithm can be viewed as an application of successive orthogonal projection algorithms, its convergence properties are investigated and the statistical behavior of the estimator is discussed in a simplified theoretical setting.

关键词： projection algorithms distributed databases algorithms signal processing Distribute Estimators data mining Distance learning learning algorithms

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Set-membership affine projection algorithm for echo cancellation

Set-membership affine projection algorithm for echo cancella...

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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： P.S.R. Diniz R.P. Braga S. Werner LPS-Signal Processing Laboratory COPPE/Poli-UFRJ Rio de Janeiro Brazil Amazonia Celular Brazil Signal Processing Laboratory Helsinki University of Technology Finland

This paper proposes a new data-selective affine projection algorithm for echo cancellation. The algorithm generalizes the concepts of the conventional set-membership affine-projection by incorporating a lower bound on the output error in order to prevent undesirable attenuation of the far-end signal. It is shown that the echo signal can more reliably be removed from the far-end user signals by employing the new algorithm in double talk situations. In addition, the proposed algorithm retains the fast convergence of the conventional SM-AP algorithm while keeping a reduced number of coefficient updates. Simulation results, using the ITU-T G.168 recommendation setup parameters, are presented in order to confirm the good features of the proposed algorithm

关键词： projection algorithms Echo cancellers Adaptive filters Computational complexity Error correction Estimation error Filtering Least squares approximation Resonance light scattering Adaptive algorithm

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Reconstruction of Vessel Axis Based on the Matching of iterative projection Algorithm and Analysis of Corresponding Points

Reconstruction of Vessel Axis Based on the Matching of itera...

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Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

作者： Wei Hong Xuanqin Mou Ying Yang Tao Luo Shaojie Tang Lingqiu Jiang Institute of Image Processing School of Electronics and Information Engineering Xi'an Jiaotong University Xi'an Shaanxi China

This paper proposes a novel method of reconstruction of vessel axis on the matching of iterative projection algorithm and analyzing of corresponding points. The 3-D space is divided into several cubes. The cubes are projected in the actual projection directions separately. If a cube-projection includes vessel axis points, it is believed that the cube includes 3-D vessel. Then we divide the cube into several smaller cubes and repeat above process until the needed precision is reached. An approximate 3-D model of vessel axis is constituted according to projections of the cubs. The corresponding relationships of vessel axis between different direction projections are analyzed according to the approximate 3-D axis model. Then we can constitute the accurate continuous 3-D vessel axis by interpolation method. We use an actual DSA sequence as the experimental data and the result is satisfactory

关键词： projection algorithms Algorithm design and analysis Image reconstruction Biomedical imaging Reconstruction algorithms Blood vessels Iterative methods Image sequences Interpolation Three dimensional displays

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