In this paper we develop two sequential or ''on-line'' estimation schemes in the time domain for dynamic shock-error models which are special cases of errors-in-variables models. Our approach utilizes ...
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In this paper we develop two sequential or ''on-line'' estimation schemes in the time domain for dynamic shock-error models which are special cases of errors-in-variables models. Our approach utilizes a state-space representation of the model, Kalman filtering techniques, and on-line algorithms. The first on-line algorithm is based on the expectation-maximization algorithm and uses a recursive Gauss-Newton scheme to maximize the Kullback Leibler information measure. The second on-line algorithm we propose is a gradient-based scheme and uses stochastic approximations to maximize the log likelihood. In comparison to the off-line Maximum Likelihood estimation scheme used in [1], our on-line algorithms have significantly reduced computational costs and negligible memory requirements. Simulations illustrate the satisfactory performance of the algorithms in estimating errors-in-variables systems with parameters that vary slowly with time or undergo infrequent jump changes.
When faced with a large support point spread function (PSF), the iterative expectation-maximization (EM) algorithm, which is often used for PSF identification, is very sensitive to the initial PSF estimate. To deal wi...
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When faced with a large support point spread function (PSF), the iterative expectation-maximization (EM) algorithm, which is often used for PSF identification, is very sensitive to the initial PSF estimate. To deal with this problem, the authors propose to do EM image identification and restoration in the subband domain. After the image is first divided into subbands, the EM algorithm is applied to each subband separately. Since the PSF can be taken to have smaller support in each subband, these subbands should be less of a problem with the EM model identification. They also introduce an adaptive subband EM method for use in the upper frequency subbands.
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.
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 maxi...
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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].
The Class A Middleton noise model is a commonly used statistical-physical, parametric model for non-Gaussian interference superimposed on a Gaussian background. In this study, the problem of efficient estimation of th...
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The Class A Middleton noise model is a commonly used statistical-physical, parametric model for non-Gaussian interference superimposed on a Gaussian background. In this study, the problem of efficient estimation of the Class A parameters for small sample sizes is considered. The proposed estimator is based on the EM algorithm, a two-step iterative estimation technique that is ideally suited for the Class A estimation problem since the observations can be readily treated as incomplete data. For the single-parameter estimation problem, a closed-form expression for the estimator is obtained. Furthermore, for the single-parameter estimation problem, it is shown that the sequence of estimates obtained via the EM algorithm converges, and a characterization of the point to which the sequence converges is given. In particular, it is shown that if the limit point of this convergent sequence is an interior point of the parameter set of interest, then it must be a stationary point of the traditional likelihood function. In addition, for both the single-parameter and two-parameter estimation problems, the small-sample-size performance of the proposed EM algorithm is examined via an extensive simulation study.
We have studied the properties of two iterative reconstruction algorithms, namely, the maximum likelihood with expectation maximization (ML-EM) and the weighted least squares with conjugate gradient (WLS-CG) algorithm...
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We have studied the properties of two iterative reconstruction algorithms, namely, the maximum likelihood with expectation maximization (ML-EM) and the weighted least squares with conjugate gradient (WLS-CG) algorithms, for use in compensation for attenuation and detector response in cardiac SPECT imaging. A realistic phantom, derived from a patient X-ray CT study to simulate 201T1 SPECT data, was used in the investigation. Both algorithms are effective in compensating for the nonuniform attenuation distribution in the thorax region and the spatially variant detector response function of the imaging system. At low iteration numbers, the addition of detector response compensation provides improvement in both spatial resolution and image noise when compared with attenuation compensation alone. However, at higher iteration numbers, there is a more rapid increase in image noise when detector response compensation is included, and the increase is more dramatic for the WLS-CG algorithm. In general, the convergence rate of the WLS-CG algorithm is about ten times that of the ML-EM algorithm. Also, the WLS-CG exhibits a faster increase in image noise at large iteration numbers than the ML-EM algorithm. This study is valuable in the search for useful and practical reconstruction methods for improved clinical cardiac SPECT imaging.
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.
A novel method of reconstruction from single-photon emission computerized tomography data is proposed. This method builds on the expectation-maximization (EM) approach to maximum likelihood reconstruction from emissio...
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A novel method of reconstruction from single-photon emission computerized tomography data is proposed. This method builds on the expectation-maximization (EM) approach to maximum likelihood reconstruction from emission tomography data, but aims instead at maximum posterior probability estimation, which takes account of prior belief about smoothness in the isotope concentration. A novel modification to the EM algorithm yields a practical method. The method is illustrated by an application to data from brain scans.
A polynomial approach for maximum-likelihood (ML) estimation of superimposed signals in time-series problems and array processing was recently proposed. This technique was applied successfully to linear uniform arrays...
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A polynomial approach for maximum-likelihood (ML) estimation of superimposed signals in time-series problems and array processing was recently proposed. This technique was applied successfully to linear uniform arrays and to uniformly sampled complex exponential signals. However, uniformly spaced arrays are not optimal for minimum variance estimation of bearing, range or position, and uniform sampling of signals is not always possible in practice. The authors make use of the expectation-maximization algorithm to apply the polynomial approach to sublattice arrays and to missing samples in time-series problems.
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...
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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.
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