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Mixed L²-Wasserstein optimal mapping between prescribed density functions

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2001年第2期111卷 255-271页

作者： Benamou, JD Brenier, Y INRIA Le Chesnay France Univ Paris 06 Anal Numer Lab F-75252 Paris France

A time-dependent minimization problem for the computation of a mixed L-2-Wasserstein distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the classical Wasserstein distance. The optimum of the cost function corresponds to an optimal mapping between prescribed initial and final densities. We enforce the final density conditions through a penalization term added to our cost function. A conjugate gradient method is used to solve this relaxed problem. We obtain an algorithm which computes an interpolated L-2-Wasserstein distance between two densities and the corresponding optimal mapping.

关键词： Monge-Kantorovitch mass transfer problem Wasserstein distance least-square distance optimal control conjugate gradient algorithm

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Spatiotemporal hierarchical Bayesian modeling: Tropical ocean surface winds

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2001年第454期96卷 382-397页

作者： Wikle, CK Milliff, RF Nychka, D Berliner, LM Univ Missouri Dept Stat Columbia MO 65211 USA Colorado Res Associates Boulder CO 80301 USA Natl Ctr Atmospher Res Geophys Stat Project Boulder CO 80307 USA Ohio State Univ Dept Stat Columbus OH 43210 USA

Spatiotemporal processes are ubiquitous in the environmental and physical sciences. This is certainly true of atmospheric and oceanic processes, which typically exhibit many different scales of spatial and temporal variability. The complexity of these processes and the large number of observation/prediction locations preclude the use of traditional covariance-based spatiotemporal statistical methods. Alternatively, we focus on conditionally specified (i.e., hierarchical) spatiotemporal models. These methods offer several advantages over traditional approaches. Primarily, physical and dynamical constraints can be easily incorporated into the conditional formulation, so that the series of relatively simple yet physically realistic conditional models leads to a much more complicated spatiotemporal covariance structure than can be specified directly. Furthermore, by making use of the sparse structure inherent in the hierarchical approach, as well as multiresolution (wavelet) bases, the models can be computed with very large datasets. This modeling approach was necessitated by a scientifically meaningful problem in the geosciences. Satellite-derived wind estimates have high spatial resolution but limited global coverage. In contrast, wind fields provided by the major weather centers provide complete coverage but have low spatial resolution. The god is to combine these data in a manner that incorporates the space-time dynamics inherent in the surface wind field. This is an essential task to enable meteorological research, because no complete high-resolution surface wind datasets exist over the world oceans. High-resolution datasets of this type are crucial for improving our understanding of global air-sea interactions affecting climate and tropical disturbances, and for driving large-scale ocean circulation models.

关键词： climate combining information conjugate gradient algorithm dynamical model fractal process Gibbs sampling numerical model ocean model satellite data turbulence wavelets

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An acceleration algorithm for image reconstruction based on continuous-discrete mapping model

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OPTICAL REVIEW 2000年第2期7卷 132-137页

作者： Yamaya, T Obi, T Yamaguchi, M Ohyama, N Tokyo Inst Technol Imaging Sci & Engn Lab Midori Ku Yokohama Kanagawa 2268503 Japan

In image reconstruction for X-ray computed tomography, images reconstructed by filtered backprojection (FBP) include systematic errors because the FBP method does not take into account some of the properties of the actual imaging system such as the divergence of X-ray beam. One solution to this problem is to use algebraic reconstruction methods, such as generalized analytic reconstruction from discrete samples and natural pixel decomposition. However, in the process of reconstruction using these methods, it is necessary to solve the linear algebraic equations which have a large coefficient matrix. In this paper, we propose a method to accelerate the iteration solving these equations by preconditioning the coefficient matrix using a polynomial function. The results of the computer simulations show the effectiveness of the proposed method.

关键词： computed tomography GARDS NPD continuous-discrete mapping model conjugate gradient algorithm preconditioning acceleration

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Adaptive beamforming based on the conjugate gradient algorithm

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 1997年第1期33卷 343-347页

作者： Mandyam, GD Ahmed, N Srinath, MD UNIV NEW MEXICO DEPT ELECT & COMP ENGNALBUQUERQUENM 87131 SO METHODIST UNIV DEPT ELECT & COMP ENGNDALLASTX 75275

Adaptive filtering using a version of the conjugate gradient (CG) method which does not involve matrix inversions and is hence computationally attractive has been presented in [1]. The method,,which uses a time average over a suitably chosen window in order to generate the required gradients, has been used in [2] for the design of an adaptive beamformer. The algorithm essentially uses time diversity to obtain improved performance. We consider a modification which essentially combines spatial and time diversity to obtain an algorithm for adaptive beamforming which has potential al,plication in cellular communication systems. Simulation results are presented to demonstrate the performance of the algorithm.

关键词： array signal processing cellular radio conjugate gradient methods digital simulation performance evaluation simulation adaptive beamforming adaptive filtering cellular communication conjugate gradient algorithm improved performance matrix inversions perf time diversity FABP9 gene Adaptive Beam forming adaptive filters simulating array signal processing Performance Evaluation matrix inversion Digital simulation Cellular communications algorithms average time conjugate gradient methods conjugate gradient

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Fast robust quasi-Newton algorithm for adaptive arrays

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IEE PROCEEDINGS-COMMUNICATIONS 1999年第4期146卷 231-239页

作者： Klemes, M Nortel Networks Dept R412 Microwave Radio Syst Dev Ottawa ON K1Y 4H7 Canada

A stable, fast (order-of-N) quasi-Newton (QN) algorithm (FRQN) applicable to arbitrary at-ray signals is presented. Its complexity is only twice that of the normalised least mean squares (NLMS) algorithm, yet its convergence is faster and smoother, proceeding along the optimal QN path as that of the order N-2 recursive least squares (RLS) algorithm, albeit more slowly. The development of its recursive update equation is outlined and compared to those of the NLMS and RLS algorithms, as well as variations of the conjugate gradient (CG) algorithm. Analytic expressions for its excess mean squared error in stationary and non-stationary scenarios are presented and compared with those of the LMS algorithm. Simulations of an adaptive array in a mobile wireless base-station show that the FRQN performance falls between that of the NLMS and RLS algorithms for a wide range of signal scenarios.

关键词： mean square error methods stable quasi-Newton algorithm normalised least mean squares adaptive signal processing computational complexity Antenna arrays radiofrequency interference mean squared error mobile wireless base-station array signals Signal processing and detection convergence recursive least squares algorithm recursive update equation Mobile radio systems nonstationary signals Electromagnetic compatibility and interference Newton method numerical stability complexity conjugate gradient algorithm NLMS algorithm interference cancellation land mobile radio Interpolation and function approximation (numerical analysis) adaptive antenna arrays digital adaptive array algorithm stationary signals fast robust quasi-Newton algorithm RLS algorithm interference suppression

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An enhanced training algorithm for multilayer neural networks based on reference output of hidden layer

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NEURAL COMPUTING & APPLICATIONS 1999年第3期8卷 218-225页

作者： Li, Y Rad, AB Peng, W Hong Kong Polytech Univ Dept Elect Engn Kowloon Peoples R China Flinders Univ S Australia Sch Engn Adelaide SA 5001 Australia

In this paper, the authors propose a new training algorithm which does nor only rely upon the training samples, but also depends upon the output of the hidden layer. We adjust both the connecting weights and outputs of the hidden layer based on Least Square Backpropagation (LSB) algorithm. A set of 'required' outputs of the hidden layer is added to the input sets through a feedback path to accelerate the convergence speed. The numerical simulation results have demonstrated that the algorithm is better than conventional BP, Quasi-Newton BFGS (an alternative to the conjugate gradient methods for fast optimisation) and LSB algorithms in terms of convergence speed and training error. The proposed method does not suffer from the drawback of the LSB algorithm, for which the training error cannot be further reduced after three iterations.

关键词： Backpropagation BFGS Quasi-Newton algorithm conjugate gradient algorithm least squares multilayer neural networks

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Learning strategies for adaptive equalizers using the constant modulus error criterion

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 1998年第2期12卷 97-116页

作者： Soni, RA Schirtzinger, TA Jenkins, WK Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA

In communication systems, data are often corrupted during transmission due to imperfect communication channels. Since channel characteristics may be time varying or unknown prior to data transmission, adaptive equalizers are typically incorporated into the receiver to reduce the ill effects of the imperfect channel. Conventional equalizers utilize a training signal to achieve the proper correction. Blind equalization schemes do not require the use of a training signal, but instead attempt restoration based upon some known property of the transmitted signal. The constant modulus algorithm (CMA) is a blind equalization technique that may be used to equalize certain communication signals (e.g. BPSK, QPSK, and FM). This paper investigates three new techniques for adaptive equalization based on the constant modulus error criterion: (i) the fast quasi-Newton CMA, (ii) the conjugate gradient quasi-Newton CMA, (iii) the conjugate gradient CMA. These three methods are formulated analytically and evaluated experimentally on several typical communication channel models. (C) 1998 John Wiley & Sons, Ltd.

关键词： adaptive channel equalization blind equalization conjugate gradient algorithm constant modulus algorithm fast quasi-Newton CMA algorithm LMS algorithm

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A parallel algorithm for pulsed laser infrared tomography

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PATTERN RECOGNITION LETTERS 1998年第5-6期19卷 521-526页

作者： Shoari, S Bagherzadeh, N Goodman, D Milner, TE Smithies, DJ Nelson, JS Univ Calif Irvine Dept Elect & Comp Engn Irvine CA 92697 USA Univ Calif Lawrence Livermore Natl Lab Livermore CA 94550 USA Univ Calif Irvine Beckman Laser Inst & Med Clin Irvine CA 92697 USA

A three-dimensional Tomographic Reconstruction algorithm (3D TRA) has been developed and implemented on a parallel machine at the Maul High Performance Computing Center (MHPCC). Given a time sequence of infrared images, this algorithm provides information to determine the location, physical dimensions, and initial space-dependent temperature increase of laser heated blood vessels. In this approach the serial computation of a 3D TRA is decomposed into multiple tasks which can be executed in parallel to reduce the computation time. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： parallel processing system performance conjugate gradient algorithm infrared image

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An efficient algorithm for large-scale nonlinear programming problems with simple bounds on the variables

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SIAM JOURNAL ON OPTIMIZATION 1998年第2期8卷 532-560页

作者： Pytlak, R Univ London Imperial Coll Sci Technol & Med Ctr Proc Syst Engn London SW7 2BT England

In this paper we present a new conjugate gradient algorithm for nonlinear programming problems with simple bounds on the variables. The method is an extension of our conjugate gradient algorithm described in [R. Pytlak, IMA J. Numer. Anal., 14 (1994), pp. 443-460]. The simple constraints on the variables are treated by a projection. Under mild assumptions the method is globally convergent. The algorithm has the property whereby many constraints can leave or enter an active set of constraints at one iteration. If the strict complementarity condition is satisfied, the active set at a solution is identified in a finite number of iterations. The algorithm has been tested on problems with more than 10,000 variables.

关键词： conjugate gradient algorithm box constraints projection large-scale problems

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Differential game approach to the mixed H-2-H-infinity problem

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1997年第6期20卷 1229-1234页

作者： Sweriduk, GD Calise, AJ GEORGIA INST TECHNOL SCH AEROSP ENGN ATLANTA GA 30332 USA

H-infinity control theory has gained wide acceptance over the past 10 years as a valuable method of controller design. However, for most applications the solution results in a controller of higher dimension than that of the plant, As an alternative to controller order reduction, low-order controllers can be designed by fixing the order of the controller a priori. There also has been a growing interest in the mixed H-2-H-infinity problem. This problem has not been resolved completely, and there are few published solutions for the fixed-order case, A differential game formulation for the H-infinity problem is extended to address the mixed problem. The result is five first-order necessary conditions, and a conjugate gradient algorithm is used to search for solutions. To test the approach, a 10th-order problem describing the lateral dynamics of a high-performance helicopter in forward flight is used.

关键词： Observability Gramian conjugate gradient algorithm Helicopters Full State Feedback Model Order Reduction Riccati Equation Method Stability Derivatives White Noise Sideslip Optimal Projection Equations

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