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 alg...
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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.
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-maximi...
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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.
The expectationmaximization (EM) algorithm is an alternative reconstruction method to the Filtered Back Projection method, providing many advantages including decreased sensitivity to noise. However the algorithm req...
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ISBN:
(纸本)9781467325332;9781467325349
The expectationmaximization (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.
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 o...
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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.
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 approximati...
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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 expectationmaximization 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.
A maximum-likelihood approach to the blur identification problem is presented. The expectation-maximization algorithm is proposed to optimize the nonlinear likelihood function in an efficient way. In order to improve ...
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A maximum-likelihood approach to the blur identification problem is presented. The expectation-maximization algorithm is proposed to optimize the nonlinear likelihood function in an efficient way. In order to improve the performance of the identification algorithm, low-order parametric image and blur models are incorporated into the identification method. The resulting iterative technique simultaneously identifies and restores noisy blurred images.< >
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 li...
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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.< >
Two algorithms are derived for the problem of tracking a manoeuvring target based on a sequence of noisy measurements of the state. Manoeuvres are modeled as unknown input (acceleration) terms entering linearly into t...
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Two algorithms are derived for the problem of tracking a manoeuvring target based on a sequence of noisy measurements of the state. Manoeuvres are modeled as unknown input (acceleration) terms entering linearly into the state equation and chosen from a discrete set. The expectationmaximization (EM) algorithm is first applied, resulting in a multi-pass estimator of the MAP sequence of inputs. The expectation step for each pass involves computation of state estimates in a bank of Kalman smoothers tuned to the possible manoeuvre sequences. The maximization computation is efficiently implemented using the Viterbi algorithm. A second, recursive estimator is then derived using a modified EM-type cost function. To obtain a dynamic programming recursion, the target state is assumed to satisfy a Markov property with respect to the manoeuvre sequence. This results in a recursive but suboptimal estimator implementable on a Viterbi trellis. The transition costs of the latter algorithm, which depend on filtered estimates of the state, are compared with the costs arising in a Viterbi-based manoeuvre estimator due to Averbuch, et al. (IEEE Transactions on Aerospace and Electronic Sytstme, 27, 3 (1991), 550-563). It is shown that the two criteria differ only in the weighting matrix of the quadratic part of the cost function. Simulations are provided to demonstrate the performance of both the batch and recursive estimators compared with Averbuch's method and the interacting multiple model (INM) filter.
The expectation-maximization (EM) method can facilitate maximizing likelihood functions that arise in statistical estimation problems. In the classical EM paradigm, one iteratively maximizes the conditional log-likeli...
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The expectation-maximization (EM) method can facilitate maximizing likelihood functions that arise in statistical estimation problems. In the classical EM paradigm, one iteratively maximizes the conditional log-likelihood of a single unobservable complete data space, rather than maximizing the intractable likelihood function for the measured or incomplete data. EM algorithms update all parameters simultaneously, which has two drawbacks: 1) slow convergence, and 2) difficult maximization steps due to coupling when smoothness penalties are used. This paper describes the space-alternating generalized EM (SAGE) method, which updates the parameters sequentially by alternating between several small hidden-data spaces defined by the algorithm designer. We prove that the sequence of estimates monotonically increases the penalized-likelihood objective, we derive asymptotic convergence rates, and we provide sufficient conditions for monotone convergence in norm. Two signal processing applications illustrate the method: estimation of superimposed signals in Gaussian noise, and image reconstruction from Poisson measurements. In both applications, our SAGE algorithms easily accommodate smoothness penalties and converge faster than the EM algorithms.
We consider the detection of a direct-sequence spread-spectrum signal received in a pulsed noise jamming environment. The expectation-maximization algorithm is used to estimate the unknown jammer parameters and hence ...
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We consider the detection of a direct-sequence spread-spectrum signal received in a pulsed noise jamming environment. The expectation-maximization algorithm is used to estimate the unknown jammer parameters and hence obtain a decision on the binary signal based on the estimated likelihood functions. The probability of error performance of the algorithm is simulated for a repeat code and a (7,4) block code. Simulation results show that at low signal-to-thermal noise ratio and high jammer power, the EM detector performs significantly better than the hard limiter and somewhat better than the soft limiter. Also, at low SNR, there is little degradation as compared to the maximum-likelihood detector with true jammer parameters. At high SNR, the soft limiter outperforms the EM detector.
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