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expectation-maximization algorithms, NULL SPACES, AND MAP IMAGE-RESTORATION

IEEE TRANSACTIONS ON IMAGE PROCESSING 1995年第8期4卷 1084-1095页

作者： HEBERT, TJ LU, KM Dept. of Electr. Eng. Houston Univ. TX.

In this paper, a computationally efficient, easily implementable algorithm for MAP restoration of images degraded by blur and additive correlated Gaussian noise using Gibbs prior density functions is derived, This algorithm is valid for a variety of complete data spaces, The constraints upon the complete data space arising from the Gaussian image formation model are analyzed and a motivation is provided for the choice of the complete data, based upon the ease of computation of the resulting EM algorithms, The overlooked role of the null space of the blur operator in image restoration is introduced, An examination of this role reveals an important drawback to the use of the simulated annealing algorithm in maximizing a specific class of functionals, An alternative iterative method for computing the nullspace component of a vector is given, The ability of a simple Gibbs prior density function to enable partial recovery of the component of an image within the nullspace of the blur operator is demonstrated.

关键词： expectation-maximization algorithms Null space Image restoration Density functional theory Iterative algorithms Degradation Additive noise Gaussian noise Image analysis Algorithm design and analysis

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Message passing expectation-maximization algorithms

Message passing expectation-maximization algorithms

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13th IEEE Workshop on Statistical Signal Processing

作者： O'Sullivan, Joseph A. Washington Univ Dept Elect & Syst Engn Elect Syst & Signals Res Lab St Louis MO 63130 USA

ISBN: (纸本)0780394038

Message passing algorithms have had dramatic impacts on important problems in signal processing, learning theory, communication theory, and information theory through their computational efficiency. expectation-maximization algorithms have had dramatic impacts on problems in estimation and detection theory, but their computational efficiency often limits their applicability. Given a bipartite graphical model for the data, if a set of hidden independent random variables can be associated with the edges, then a resulting expectation-maximization algorithm is message passing on this graph. The algorithms are computationally efficient in the same sense as other message passing algorithms. One example of such algorithms is the standard expectation-maximization algorithm for emission tomography. Another example for a signal in Gaussian noise yields a statistical interpretation to efficient algorithms for sparse linear inverse problems.

关键词： Message passing expectation-maximization algorithms Signal processing algorithms Computational efficiency Information theory Estimation theory Bipartite graph Random variables Tomography Gaussian noise

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ON THE IMPLEMENTATION AND ANALYSIS OF expectation maximization algorithms WITH STOPPING CRITERIONmaximization

ON THE IMPLEMENTATION AND ANALYSIS OF EXPECTATION MAXIMIZATI...

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19th IEEE International Conference on Image Processing (ICIP)

作者： Ryan, Andrew Mora, Benjamin Chen, Min Swansea Univ Coll Sci Dept Comp Sci Swansea W Glam Wales Univ Oxford Oxford E Res Ctr Oxford England

ISBN: (纸本)9781467325332;9781467325349

The expectation maximization (EM) algorithm is an alternative reconstruction method to the Filtered Back Projection method, providing many advantages including decreased sensitivity to noise. However the algorithm requires a large number of iterations to reach adequate convergence. Due to this, research has been carried out into accelerating the convergence rate of the EM algorithm. In this paper we present an analysis of an EM implementation which uses both OSEM and MGEM, comparing results on a per time basis with both acceleration techniques alone as well as a combination of the two methods. We provide an alternative stopping criterion based on the RMS error of the projections of the current reconstruction and compare the result with an existing variance based approach.

关键词： Reconstruction algorithms Computed tomography expectation-maximization algorithms Mean square error methods Acceleration techniques

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An Accurate, Fast Approximation for the Sum of Fading Random Variables via expectation maximization Applications to Diversity Systems

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IEEE ACCESS 2018年 6卷 42616-42630页

作者： Vega Sanchez, Jose David Urquiza-Aguiar, Luis Paredes Paredes, Martha Cecilia Escuela Politec Nacl Dept Elect Telecomunicac & Redes Informac Fac Elect & Elect Quito 170525 Ecuador

Sums of fading envelopes occur in several wireless communications applications. The exact mathematical solution to this statistic is, however, rather intricate. In this paper, we derive a novel closed-form approximation to the sum of not necessarily identically distributed Nakagami-m random variables. The necessary parameters of the approximate solution are estimated by using the well-known expectation maximization algorithm with a Nakagami-m mixture model. The proposed approximation finds applicability in obtaining important performance metrics of communications systems where sums of variates arise. More specifically, we apply the proposed method to derive a closed-form expression for average bit error probability (ABEP) of multibranch equal-gain combining receivers. The presented models are general and can be applied to any modulation scheme. Furthermore, simplified asymptotic closed-form expressions for the ABEP have been derived to examine the achievable diversity and coding gains. Finally, the performance of the proposed approach is verified by comparing itself against both the exact evaluation and the previous results in the literature.

关键词： Approximation methods diversity systems expectation-maximization algorithms Nakagami-m distribution performance analysis

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ITERATIVE RECONSTRUCTION-REPROJECTION AND THE expectation-maximization ALGORITHM

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IEEE TRANSACTIONS ON MEDICAL IMAGING 1990年第1期9卷 94-98页

作者： OLLINGER, JM HOSP UNIV PENN DEPT NUCL MEDPHILADELPHIAPA 19104

The iterative reconstruction-reprojection (IRR) algorithm is a method for estimating missing projections in computed tomography. It is derived as an expectation-maximization (EM) algorithm that increases a suitable likelihood function. The constraint that the data form a consistent set of projections is loosened to require only that the means of the data form a consistent set, thereby suggesting that the algorithm is suitable for use with noisy data. Proofs of convergence to a stationary point and of monotonicity of the sequence of iterates are given. Simulations supporting these results are described.< >

关键词： expectation-maximization algorithms Image reconstruction Iterative algorithms Computed tomography Iterative methods Positron emission tomography Maximum likelihood estimation Image analysis Algorithm design and analysis

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Improved expectation maximization Algorithm for Gaussian Mixed Model Using the Kernel Method

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MATHEMATICAL PROBLEMS IN ENGINEERING 2013年第1期2013卷 1-9页

作者： Yusoff, Mohd Izhan Mohd Mohamed, Ibrahim Abu Bakar, Mohd Rizam Univ Malaya Inst Math Sci Kuala Lumpur 50603 Malaysia Telekom Res & Dev Sdn Bhd Cyberjaya 63000 Selangor Malaysia Univ Putra Malaysia Dept Math Serdang 43400 Malaysia

Fraud activities have contributed to heavy losses suffered by telecommunication companies. In this paper, we attempt to use Gaussian mixed model, which is a probabilistic model normally used in speech recognition to identify fraud calls in the telecommunication industry. We look at several issues encountered when calculating the maximum likelihood estimates of the Gaussian mixed model using an expectation maximization algorithm. Firstly, we look at a mechanism for the determination of the initial number of Gaussian components and the choice of the initial values of the algorithm using the kernel method. We show via simulation that the technique improves the performance of the algorithm. Secondly, we developed a procedure for determining the order of the Gaussian mixed model using the log-likelihood function and the Akaike information criteria. Finally, for illustration, we apply the improved algorithm to real telecommunication data. The modified method will pave the way to introduce a comprehensive method for detecting fraud calls in future work.

关键词： expectation-maximization algorithms GAUSSIAN processes KERNEL (Mathematics) TELECOMMUNICATION COMPUTER simulation AKAIKE information criterion

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A genetic expectation-maximization method for unsupervised change detection in multitemporal SAR imagery

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INTERNATIONAL JOURNAL OF REMOTE SENSING 2009年第24期30卷 6591-6610页

作者： Bazi, Yakoub Melgani, Farid Bruzzone, Lorenzo Vernazza, Gianni Univ Trent Dept Comp Sci & Informat Engn I-38050 Trento Italy Al Jouf Univ Coll Engn Al Jouf 2014 Saudi Arabia Univ Genoa Dept Biophys & Elect Engn I-16145 Genoa Italy

In this paper, we present a novel, automatic and unsupervised change-detection approach to the analysis of single-channel single-polarization multitemporal SAR images. The statistical parameters of the changed and unchanged classes, which are assumed to follow a generalized Gaussian (GG) distribution in the analysed log-ratio image, are explicitly estimated by the expectation-maximization (EM) algorithm initialized with a robust strategy based on genetic algorithms (GAs). In addition, the proposed approach integrates two further processing capabilities. The first one intends to cope with the problem of the automatic detection of multiple changes in the scene. This is carried out by modelling the log-ratio image histogram with a multimodal GG mixture whose number of components is estimated basing on the Bayesian information criterion (BIC). The second processing capability allows exploitation of spatial contextual information in the change detection process through a Markovian formulation. Results obtained on both simulated and real data are reported and discussed.

关键词： expectation-maximization algorithms REMOTE sensing GENETIC algorithms GAUSSIAN distribution COMBINATORIAL optimization OPTICAL polarization DISTRIBUTION (Probability theory) EARTH (Planet) SURFACE

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Direct maximization of the likelihood of a hidden Markov model

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2008年第9期52卷 4147-4160页

作者： Turner, Rolf Univ Auckland Starpath Project Auckland 1 New Zealand Univ New Brunswick Dept Math & Stat Fredericton NB E3B 5A3 Canada

Ever since the introduction of hidden Markov models by Baum and his co-workers, the method of choice for fitting such models has been maximum likelihood via the EM algorithm. In recent years it has been noticed that the gradient and Hessian of the log likelihood of hidden Markov and related models may be calculated in parallel with a filtering process by which the likelihood may be calculated. Various authors have used, or suggested the use of, this idea in order to maximize the likelihood directly, without using the EM algorithm. In this paper we discuss an implementation of such an approach. We have found that a straightforward implementation of Newton's method sometimes works but is unreliable. A form of the Levenberg-Marquardt algorithm appears to provide excellent reliability. Two rather complex examples are given for applying this algorithm to the fitting of hidden Markov models. In the first a better than 6-fold increase in speed over the EM algorithm was achieved. The second example turned out to be problematic (somewhat interestingly) in that the maximum likelihood estimator appears to be inconsistent. Whatever its merit, this estimator is calculated much faster by Levenberg-Marquardt than by EM. We also compared the Levenberg-Marquardt algorithm, applied to the first example, with a generic numerical maximization procedure. The Levenberg-Marquardt algorithm appeared to perform almost three times better than the generic procedure, even when analytic derivatives were provided, and 19 times better when they were not provided. (c) 2008 Elsevier B.V All rights reserved.

关键词： MARKOV processes STOCHASTIC processes HIDDEN Markov models expectation-maximization algorithms

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Radial basis function networks, regression weights, and the expectation-maximization algorithm

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART A-SYSTEMS AND HUMANS 1997年第5期27卷 613-623页

作者： Langari, R Wang, L Yen, J Center for Fuzzy Logic Robotics and Intelligent Systems Texas A and M University College Station TX USA

We propose a modified radial basis function (RBF) network in which the regression weights are used to replace the constant weights in the output layer, It is shown that the modified RBF network can reduce the number of hidden units significantly. A computationally efficient algorithm, known as the expectation-maximization (EM) algorithm, is used to estimate the parameters of the regression weights, A salient feature of this algorithm is that it decomposes a complicated multiparameter optimization problem into L separate small-scale optimization problems, where L is the number of hidden units, The superior performance of the modified RBF network over the standard RBF network is illustrated by computer simulations.

关键词： Radial basis function networks expectation-maximization algorithms Signal processing algorithms Iterative algorithms Intelligent robots Parameter estimation Computer simulation Process control Biomedical signal processing Pattern recognition

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THE expectation-maximization ALGORITHM FOR SYMBOL UNSYNCHRONIZED SEQUENCE DETECTION

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IEEE TRANSACTIONS ON COMMUNICATIONS 1991年第1期39卷 54-61页

作者： GEORGHIADES, CN SNYDER, DL WASHINGTON UNIV FAC ELECT ENGNDEPT ELECT ENGNST LOUISMO 63130

The expectation-maximization (EM) algorithm for maximizing likelihood functions, combined with the Viterbi algorithm, is applied to the problem of sequence detection when symbol timing information is not present. Although the EM algorithm is noncausal, results obtained using the algorithm on the problem of nonsynchronized sequence detection indicate that it converges most of the time in three iterations, making it both of theoretical as well as practical interest. Finally, a practical algorithm based on the EM algorithm is introduced, which reduces the computational burden and improves performance by making use of timing estimates in previous observation windows.

关键词： expectation-maximization algorithms Timing Maximum likelihood estimation Iterative algorithms Statistics Sampling methods Viterbi algorithm Maximum likelihood detection Performance analysis Algorithm design and analysis

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