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Wiener extrapolation of sequences and the expectation-maximization algorithm

IEEE SIGNAL PROCESSING LETTERS 1996年第9期3卷 260-262页

作者： ArtesRodriguez, A FigueirasVidal, AR UNIV CARLOS III MADRID EPS TELECOMMADRIDSPAIN

The application, of the expectation-maximization (EM) algorithm to estimate the signal autocorrelation in Wiener extrapolation allows us to view previous techniques as particular cases, to modify them, and to introduc... 详细信息

关键词： bockwurst Sequences extrapolation method expectation-maximisation algorithm

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GLOBALLY CONVERGENT algorithmS FOR MAXIMUM A-POSTERIORI TRANSMISSION TOMOGRAPHY

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IEEE TRANSACTIONS ON IMAGE PROCESSING 1995年第10期4卷 1430-1438页

作者： LANGE, K FESSLER, JA UNIV MICHIGAN DEPT INTERNAL MED DIV NUCL MED ANN ARBOR MI 48109 USA

This paper reviews and compares three maximum likelihood algorithms for transmission tomography, One of these algorithms is the EM algorithm, one is based on a convexity argument devised by De Pierro in the context of emission tomography, and one is an ad hoc gradient algorithm, The algorithms enjoy desirable local and global convergence properties and combine gracefully with Bayesian smoothing priors, Preliminary numerical testing of the algorithms on simulated data suggest that the convex algorithm and the ad hoc gradient algorithm are computationally superior to the EM algorithm, This superiority stems from the larger number of exponentiations required by the EM algorithm, The convex and gradient algorithms are well adapted to parallel computing.

关键词： global convergence Convexity expectation-maximisation algorithm Maximum a posteriori estimation algorithms simulated data Tomography, X-Ray emission tomography ad hoc

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Latency probability estimation of non-linear systems with one-step randomly delayed measurements

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IET CONTROL THEORY AND APPLICATIONS 2016年第7期10卷 843-852页

作者： Huang, Yulong Zhang, Yonggang Li, Ning Harbin Engn Univ Dept Automat Harbin 150001 Peoples R China

In this study, the authors focus on estimating the unknown constant latency probability of non-linear systems with one-step randomly delayed measurements using maximum likelihood (ML) criterion. A new latency probability estimation algorithm is proposed based on an expectation maximisation approach to obtain an approximate ML estimation of latency probability. The proposed algorithm consists of expectation step (E-step) and the maximisation step (M-step). In the E-step, the expectation of the complete data log-likelihood function is approximately computed based on the currently estimated latency probability, and in the M-step, the approximate expectation is maximised using the Newton approach. The efficacy of the proposed algorithm is illustrated in a numerical example concerning univariate non-stationary growth model.

关键词： probability nonlinear systems delays maximum likelihood estimation expectation-maximisation algorithm Newton method nonlinear systems one-step randomly delayed measurements unknown constant latency probability estimation algorithm maximum likelihood criterion ML criterion expectation maximisation approach expectation step E-step maximisation step M-step complete data log-likelihood function Newton approach univariate nonstationary growth model

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Evaluation of OS-EM vs ML-EM for 1D, 2D and fully 3D SPECT reconstruction

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 1996年第3期43卷 2018-2024页

作者： Kamphuis, C Beekman, FJ Viergever, MA UNIV UTRECHT HOSP IMAGING CTRUTRECHTNETHERLANDS

For SPECT reconstruction, iterative Maximum Likelihood expectation Maximization (ML-EM) estimation has a huge computational burden. The objective of this paper is to compare images obtained by ML-EM and an EM algorithm acting on Ordered Subsets of projections (OS-EM). Two digital phantoms, a cylinder with two cold spots and an ellipsoid with several hot spots and one cold spot were reconstructed from 120 simulated noisy projections. 1D (delta-like point source response), 2D (single slice response) and fully 3D reconstruction were investigated. Three quantities were calculated for the evaluation, viz. contrast, normalized standard deviation and mean squared error. In the case of fully 3D reconstruction, OS-EM 60 reconstructions (i.e., using 60 ordered subsets) were very close to ML-EM reconstructions. This shows that the OS-EM algorithm is an extremely fast and efficient method to accelerate iterative SPECT reconstruction with speed-up factors of close to half the number of projections.

关键词： expectation-maximisation algorithm COLD SPOT single photon emission computed tomography three-dimensional displays

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A GENERALIZED EM algorithm FOR 3-D BAYESIAN RECONSTRUCTION FROM POISSON DATA USING GIBBS PRIORS

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IEEE TRANSACTIONS ON MEDICAL IMAGING 1989年第2期8卷 194-202页

作者： HEBERT, T LEAHY, R Signal and Image Processing Institute. Department of Electrical Engineering-Systems University of Southern California Los Angeles CA USA

A generalized expectation-maximization (GEM) algorithm is developed for Bayesian reconstruction, based on locally correlated Markov random-field priors in the form of Gibbs functions and on the Poisson data model. For the M-step of the algorithm, a form of coordinate gradient ascent is derived. The algorithm reduces to the EM maximum-likelihood algorithm as the Markov random-field prior tends towards a uniform distribution. Three different Gibbs function priors are examined. Reconstructions of 3-D images obtained from the Poisson model of single-photon-emission computed tomography are presented.

关键词： Three-Dimensional Images expectation-maximisation algorithm Markov algorithms Sim\'eon Denis Poisson Generalized EM algorithm Bayesian inference single photon emission computed tomography Gibbs function

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Improved analysis of greedy block coordinate descent under RIP

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ELECTRONICS LETTERS 2015年第6期51卷 488-489页

作者： Li, Haifeng Ma, Yingbin Liu, WenAn Fu, Yuli Henan Normal Univ Coll Math & Informat Sci Xinxiang 453007 Peoples R China S China Univ Technol Sch Elect & Informat Engn Guangzhou 510640 Guangdong Peoples R China

A more relaxed condition means that fewer of measurements are needed to ensure the exact sparse recovery from the theoretical aspect. The sufficient condition for the greedy block coordinate descent (GBCD) algorithm is relaxed using the near-orthogonality property. It is also shown that the GBCD algorithm fails when (1/(root K+1)<=delta(K+1)<1).

关键词： mixture models expectation-maximisation algorithm signal reconstruction approximation theory pattern clustering Bayes methods Gaussian processes model selection mixture model integrated nested Laplace approximation signal partition signal clustering expectation-and-maximisation variational approximation parametric probability density function Gaussian MM clustering Bayesian framework Monte Carlo simulation INLA EM method

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Maximum-likelihood multiresolution laser radar range imaging

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IEEE TRANSACTIONS ON IMAGE PROCESSING 1997年第1期6卷 36-46页

作者： Greer, DR Fung, I Shapiro, JH MIT DEPT ELECT ENGN & COMP SCICAMBRIDGEMA 02139 MIT ELECT RES LABCAMBRIDGEMA 02139 CENTRA SOFTWARE CAMBRIDGEMA 02138

Maximum-likelihood range imaging is considered for pulsed-imager operation of a coherent laser radar, The expectation-maximization (EM) algorithm is used to develop an explicit procedure for maximum-likelihood fitting of a multiresolution (wavelet) basis-at a sequence of increasingly fine resolutions-to laser radar range data, Specialization to the Haar-wavelet basis yields a procedure that is both computationally efficient and numerically robust. Basic analytical properties of the estimation algorithm and its performance are presented, along with results based on simulated and real laser radar range data, It is shown that the weights associated with the expectation-maximization iterations provide a reliable indicator for terminating the coarse-to-fine resolution progression, At the weight-determined stopping point, estimation performance approaches the ultimate limit set by the complete-data bound.

关键词： wavelet basis parking sites maximum likelihood expectation-maximisation algorithm Lidar simulating ultimate limits

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Sharp quadratic majorization in one dimension

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2009年第7期53卷 2471-2484页

作者： de Leeuw, Jan Lange, Kenneth Univ Calif Los Angeles Dept Stat Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Biomath Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Human Genet Los Angeles CA 90095 USA

Majorization methods solve minimization problems by replacing a complicated problem by a sequence of simpler problems. Solving the sequence of simple optimization problems guarantees convergence to a solution of the complicated original problem. Convergence is guaranteed by requiring that the approximating functions majorize the original function at the current solution. The leading examples of majorization are the EM algorithm and the SMACOF algorithm used in Multidimensional Scaling. The simplest possible majorizing subproblems are quadratic, because minimizing a quadratic is easy to do. In this paper quadratic majorizations for real-valued functions of a real variable are analyzed, and the concept of sharp majorization is introduced and studied. Applications to logit, probit, and robust loss functions are discussed. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Multi dimensional scaling Converge Check a Solution Solutions expectation-maximisation algorithm LOSS FUNCTION Verify a Solution Quadratic original problem ACD-A solution real variables

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Hierarchical adaptive Kalman filtering for interplanetary orbit determination

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 1998年第3期34卷 883-896页

作者： Chaer, WS Bishop, RH Ghosh, J Univ Texas Dept Aerosp Engn & Engn Mech Austin TX 78712 USA Univ Texas Dept Elect & Comp Engn Austin TX 78712 USA

A modular and flexible approach to adaptive Kalman filtering has recently been introduced using the framework of a mixture-of-experts regulated by a gating network. Each expert is a Kalman biter modeled with a different realization of the unknown system parameters. The unknown or uncertain parameters can include elements of the state transition matrix, observation mapping matrix, process noise covariance matrix, and measurement noise covariance matrix. The gating network performs on-line adaptation of the weights given to individual filters based on performance. The mixture-of-experts approach Is extended here to a hierarchical architecture which involves multiple levels of gating. The proposed architecture provides a multilevel hypothesis testing capability, The utility of the hierarchical architecture is illustrated via the problem of interplanetary navigation (Mars Pathfinder) using simulated radiometric data, It serves as a useful tool for assisting navigation teams in the process of selecting the parameters of the navigational biter over various operating regimes. it is shown that the scheme has the capability of detecting changes in the system parameters and switching filters appropriately for optimal performance. Furthermore, the expectation-maximization (EM) algorithm is shown to be applicable in the proposed framework.

关键词： adaptive Kalman filters iterative methods learning (artificial intelligence) maximum likelihood estimation navigation neural net architecture realisation theory state estimation tracking filters Mars Pathfinder expectation-maximization algorithm gating n expectation-maximisation algorithm system parameter maximum likelihood estimation iterative methods adaptive Kalman filters navigation tracking filters neural net architecture Mars Pathfinder State estimation realisation theory

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ON COMPLETE-DATA SPACES FOR PET RECONSTRUCTION algorithmS

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 1993年第4期40卷 1055-1061页

作者： FESSLER, JA CLINTHORNE, NH ROGERS, WL Univ of Michigan Ann Arbor MI USA

As investigators consider more' comprehensive measurement models for emission tomography, there will be more choices for the complete-data spaces of the associated expectation-maximization (EM) algorithms for maximum-likelihood (ML) estimation. In this paper, we show that EM algorithms based on smaller complete-data spaces will typically converge faster. We discuss two practical applications of these concepts: (i) the ML-IA and ML-IB image reconstruction algorithms of Politte and Snyder [1] which are based on measurement models that account for attenuation and accidental coincidences in positron-emission tomography (PET), and (ii) the problem of simultaneous estimation of emission and transmission parameters. Although the PET applications may often violate the necessary regularity conditions, our analysis predicts heuristically that the ML-IB algorithm, which has a smaller complete-data space, should converge faster than ML-IA. This is corroborated by the empirical findings in [1].

关键词： Converge expectation-maximisation algorithm algorithms emission tomography maximum likelihood estimation transmission parameter Coincidence

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