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A STOCHASTIC steepest-descent algorithm

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1988年第2期59卷 307-323页

作者： WARDI, Y 1.School of Electrical Engineering Georgia Institute of Technology Atlanta Georgia

A stochastic steepest-descent algorithm for function minimization under noisy observations is presented. Function evaluation is done by performing a number of random experiments on a suitable probability space. The number of experiments performed at a point generated by the algorithm reflects a balance between the conflicting requirements of accuracy and computational complexity. The algorithm uses an adaptive precision scheme to determine the number of random experiments at a point; this number tends to increase whenever a stationary point is approached and to decrease otherwise. Two rules are used to determine the number of random experiments at a point; one, in the inner loop of the algorithm, uses the magnitude of the observed gradient of the function to be minimized; and the other, in the outer-loop, uses a measure of accumulated errors in function evaluations at past points generated by the algorithm. Once a stochastic approximation of the function to be minimized is obtained at a point, the algorithm proceeds to generate the next point by using the steepest-descent deterministic methods of Armijo and Polak (Refs. 3, 4). Convergence of the algorithm to stationary points is demonstrated under suitable assumptions.

关键词： steepest-descent algorithm Armijo stepsize adaptive precision schemes stochastic algorithms

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Matching parameter estimation by using the radial basis function interpolation

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IET IMAGE PROCESSING 2012年第4期6卷 407-416页

作者： Fuji, Y. Abe, Y. Iiguni, Y. Osaka Univ Grad Sch Engn Sci Toyonaka Osaka 5608531 Japan

A matching parameter estimation method with subpixel accuracy is derived by using the radial basis function (RBF) interpolation. This method reconstructs two analogue images from two given digital images by the RBF, and then minimises a non-linear cost function by the steepest-descent algorithm to estimate translation, rotation, scaling factor and intensity change between the two analogue images. The RBF provides accurate interpolation, resulting in accurate estimation. A Gaussian weighting function is introduced into the cost function to provide a local estimate within a region of interest (ROC). Then double integrals included in the cost function are analytically computed and the computational complexity is significantly reduced by exploiting the property that the Gaussian function decays rapidly. When the matching parameters are not constant over the whole image, or equivalently, the ROC is set to be small, the proposed method is better than the conventional phase correlation method in estimation accuracy.

关键词： Gaussian weighting function rotation estimation matching parameter estimation method image registration double-integrals image reconstruction scaling factor nonlinear cost function radial basis function interpolation Computer vision and image processing techniques intensity change translation estimation Optical, image and video signal processing phase correlation method analogue image reconstruction image matching subpixel accuracy digital images Interpolation and function approximation (numerical analysis) RBF interpolation interpolation steepest-descent algorithm computational complexity estimation accuracy gradient methods

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Separable nonlinear least-squares methods for efficient off-line and on-line modeling of systems using Kautz and Laguerre filters

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2001年第6期48卷 562-579页

作者： Ngia, LSH Chalmers Univ Technol Signal Proc Grp Dept Signals & Syst SE-41296 Gothenburg Sweden

Kautz and Laguerre filters are effective linear regression models that can describe accurately an unknown linear system with a fewer parameters than finite-impulse response (FIR) filters. This is achieved by expanding the transfer functions of the Kautz and Laguerre filters around some a priori knowledge, concerning the dominating time constants or resonant modes of the system to be identified. When the estimation of these filters is based on a minimization of the least-squares error criterion, the minimization problem becomes separable with respect to the linear coefficients. Therefore, the original unseparated problem can be reduced to a separated problem in only the nonlinear poles, which is numerically better conditioned than the original unseparated one. This paper proposed batch and recursive algorithms that are derived using this separable nonlinear least-squares method, for the estimation of the coefficients and poles of Kautz and Laguerre filters. They have similar computational loads, but better convergence properties than their corresponding algorithms that solve the unseparated problem. The performance of the suggested algorithms is compared to alternative batch and recursive algorithms in some system identification examples. Generally, it is shown that the proposed batch and recursive algorithms have better convergence properties than the alternatives.

关键词： echo cancelation Gauss-Newton algorithm Kautz filter Laguerre filter off-line estimation on-line estimation separable nonlinear least-squares steepest-descent algorithm

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MODELING OF ATMOSPHERIC DISTURBANCES IN METEOROLOGICAL PICTURES

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1984年第5期6卷 587-600页

作者： BOUTHEMY, P BENVENISTE, A INRS TELECOMMUN DEPT VISUAL COMMUNMONTREALQUEBECCANADA

This paper describes a model-based approach to perform tracking of extratropical atmospheric disturbances from a sequence of satellite cloud-cover images. More precisely, it deals with the estimation of motion of these spiral-shaped cloud systems (both translational and rotational motion), and the measurement of the evolution of their shape. Tracking is achieved by recording from one image to the next the changes of the model parameter values. A maximum likelihood criterion is used in the process of fitting model to sensed data. The defined model takes into account geometric and intensity aspects. Such an approach readily yields global information on the disturbance cloud system of interest. As a requirement in such an application is robustness to noise, to this end two versions of the modeling have been considered.

关键词： Atmospheric modeling Meteorology Clouds Shape measurement Satellites Motion estimation Atmospheric measurements Motion measurement Rotation measurement Maximum likelihood estimation Author Keywords tracking Cloud maximum likelihood meteorology modeling motion estimation satellite image shape steepest-descent algorithm

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