Showing papers on "Maximum a posteriori estimation published in 1997"

Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images

Abstract: The three main tools in the single image restoration theory are the maximum likelihood (ML) estimator, the maximum a posteriori probability (MAP) estimator, and the set theoretic approach using projection onto convex sets (POCS). This paper utilizes the above known tools to propose a unified methodology toward the more complicated problem of superresolution restoration. In the superresolution restoration problem, an improved resolution image is restored from several geometrically warped, blurred, noisy and downsampled measured images. The superresolution restoration problem is modeled and analyzed from the ML, the MAP, and POCS points of view, yielding a generalization of the known superresolution restoration methods. The proposed restoration approach is general but assumes explicit knowledge of the linear space- and time-variant blur, the (additive Gaussian) noise, the different measured resolutions, and the (smooth) motion characteristics. A hybrid method combining the simplicity of the ML and the incorporation of nonellipsoid constraints is presented, giving improved restoration performance, compared with the ML and the POCS approaches. The hybrid method is shown to converge to the unique optimal solution of a new definition of the optimization problem. Superresolution restoration from motionless measurements is also discussed. Simulations demonstrate the power of the proposed methodology.

Joint MAP registration and high-resolution image estimation using a sequence of undersampled images

Abstract: In many imaging systems, the detector array is not sufficiently dense to adequately sample the scene with the desired field of view. This is particularly true for many infrared focal plane arrays. Thus, the resulting images may be severely aliased. This paper examines a technique for estimating a high-resolution image, with reduced aliasing, from a sequence of undersampled frames. Several approaches to this problem have been investigated previously. However, in this paper a maximum a posteriori (MAP) framework for jointly estimating image registration parameters and the high-resolution image is presented. Several previous approaches have relied on knowing the registration parameters a priori or have utilized registration techniques not specifically designed to treat severely aliased images. In the proposed method, the registration parameters are iteratively updated along with the high-resolution image in a cyclic coordinate-descent optimization procedure. Experimental results are provided to illustrate the performance of the proposed MAP algorithm using both visible and infrared images. Quantitative error analysis is provided and several images are shown for subjective evaluation.

Statistical approach to segmentation of single-channel cerebral MR images

Abstract: A statistical model is presented that represents the distributions of major tissue classes in single-channel magnetic resonance (MR) cerebral images. Using the model, cerebral images are segmented into gray matter, white matter, and cerebrospinal fluid (CSF). The model accounts for random noise, magnetic field inhomogeneities, and biological variations of the tissues. Intensity measurements are modeled by a finite Gaussian mixture. Smoothness and piecewise contiguous nature of the tissue regions are modeled by a three-dimensional (3-D) Markov random field (MRF). A segmentation algorithm, based on the statistical model, approximately finds the maximum a posteriori (MAP) estimation of the segmentation and estimates the model parameters from the image data. The proposed scheme for segmentation is based on the iterative conditional modes (ICM) algorithm in which measurement model parameters are estimated using local information at each site, and the prior model parameters are estimated using the segmentation after each cycle of iterations. Application of the algorithm to a sample of clinical MR brain scans, comparisons of the algorithm with other statistical methods, and a validation study with a phantom are presented. The algorithm constitutes a significant step toward a complete data driven unsupervised approach to segmentation of MR images in the presence of the random noise and intensity inhomogeneities.

Optimal and Sub-optimal Maximum A-Posteriori Algorithms Suitable for Turbo-Decoding.

Abstract: For estimating the states or outputs of a Markov process, the symbol-by-symbol maximum a posteriori (MAP) algorithm is optimal. However, this algorithm, even in its recursive form, poses technical difficulties because of numerical representation problems, the necessity of non-linear functions and a high number of additions and multiplications. MAP like algorithms operating in the logarithmic domain presented in the past solve the numerical problem and reduce the computational complexity, but are suboptimal especially at low SNR (a common example is the Max-Log-MAP because of its use of the max function). A further simplification yields the soft-output Viterbi algorithm (SOVA). In this paper, we present a Log-MAP algorithm that avoids the approximations in the Max-Log-MAP algorithm and hence is equivalent to the true MAP, but without its major disadvantages. We compare the (Log-)MAP, Max-Log-MAP and SOVA from a theoretical point of view to illuminate their commonalities and differences. As a practical example, we consider Turbo decoding, and we also demonstrate the practical suitability of the Log-MAP by including quantization effects. The SOVA is, at 10−4, approximately 0.7 dB inferior to the (Log-)MAP, the Max-Log-MAP lying roughly in between. The channel capacities of the three algorithms -when employed in a Turbo decoder- are evaluated numerically.

Bayesian color constancy.

Abstract: The problem of color constancy may be solved if we can recover the physical properties of illuminants and surfaces from photosensor responses. We consider this problem within the framework of Bayesian decision theory. First, we model the relation among illuminants, surfaces, and photosensor responses. Second, we construct prior distributions that describe the probability that particular illuminants and surfaces exist in the world. Given a set of photosensor responses, we can then use Bayes’s rule to compute the posterior distribution for the illuminants and the surfaces in the scene. There are two widely used methods for obtaining a single best estimate from a posterior distribution. These are maximum a posteriori (MAP) and minimum mean-squared-error (MMSE) estimation. We argue that neither is appropriate for perception problems. We describe a new estimator, which we call the maximum local mass (MLM) estimate, that integrates local probability density. The new method uses an optimality criterion that is appropriate for perception tasks: It finds the most probable approximately correct answer. For the case of low observation noise, we provide an efficient approximation. We develop the MLM estimator for the color-constancy problem in which flat matte surfaces are uniformly illuminated. In simulations we show that the MLM method performs better than the MAP estimator and better than a number of standard color-constancy algorithms. We note conditions under which even the optimal estimator produces poor estimates: when the spectral properties of the surfaces in the scene are biased. © 1997 Optical Society of America [S0740-3232(97)01607-4]

A Bayesian approach to introducing anatomo-functional priors in the EEG/MEG inverse problem

Abstract: We present a new approach to the recovering of dipole magnitudes in a distributed source model for magnetoencephalographic (MEG) and electroencephalographic (EEG) imaging. This method consists in introducing spatial and temporal a priori information as a cure to this ill-posed inverse problem. A nonlinear spatial regularization scheme allows the preservation of dipole moment discontinuities between some a priori noncorrelated sources, for instance, when considering dipoles located on both sides of a sulcus. Moreover, we introduce temporal smoothness constraints on dipole magnitude evolution at time scales smaller than those of cognitive processes. These priors are easily integrated into a Bayesian formalism, yielding a maximum a posteriori (MAP) estimator of brain electrical activity. Results from EEG simulations of our method are presented and compared with those of classical quadratic regularization and a now popular generalized minimum-norm technique called low-resolution electromagnetic tomography (LORETA).

Efficient Approximations for the MarginalLikelihood of Bayesian Networks with Hidden Variables

Abstract: We discuss Bayesian methods for model averaging and model selection among Bayesian-network models with hidden variables. In particular, we examine large-sample approximations for the marginal likelihood of naive-Bayes models in which the root node is hidden. Such models are useful for clustering or unsupervised learning. We consider a Laplace approximation and the less accurate but more computationally efficient approximation known as the Bayesian Information Criterion (BIC), which is equivalent to Rissanen‘s (1987) Minimum Description Length (MDL). Also, we consider approximations that ignore some off-diagonal elements of the observed information matrix and an approximation proposed by Cheeseman and Stutz (1995). We evaluate the accuracy of these approximations using a Monte-Carlo gold standard. In experiments with artificial and real examples, we find that (1) none of the approximations are accurate when used for model averaging, (2) all of the approximations, with the exception of BIC/MDL, are accurate for model selection, (3) among the accurate approximations, the Cheeseman–Stutz and Diagonal approximations are the most computationally efficient, (4) all of the approximations, with the exception of BIC/MDL, can be sensitive to the prior distribution over model parameters, and (5) the Cheeseman–Stutz approximation can be more accurate than the other approximations, including the Laplace approximation, in situations where the parameters in the maximum a posteriori configuration are near a boundary.

Approximate maximum likelihood hyperparameter estimation for Gibbs priors

Abstract: The parameters of the prior, the hyperparameters, play an important role in Bayesian image estimation. Of particular importance for the case of Gibbs priors is the global hyperparameter, /spl beta/, which multiplies the Hamiltonian. Here we consider maximum likelihood (ML) estimation of /spl beta/ from incomplete data, i.e., problems in which the image, which is drawn from a Gibbs prior, is observed indirectly through some degradation or blurring process. Important applications include image restoration and image reconstruction from projections. Exact ML estimation of /spl beta/ from incomplete data is intractable for most image processing. Here we present an approximate ML estimator that is computed simultaneously with a maximum a posteriori (MAP) image estimate. The algorithm is based on a mean field approximation technique through which multidimensional Gibbs distributions are approximated by a separable function equal to a product of one-dimensional (1-D) densities. We show how this approach can be used to simplify the ML estimation problem. We also show how the Gibbs-Bogoliubov-Feynman (GBF) bound can be used to optimize the approximation for a restricted class of problems. We present the results of a Monte Carlo study that examines the bias and variance of this estimator when applied to image restoration.

Expectation maximization reconstruction of positron emission tomography images using anatomical magnetic resonance information

Abstract: Using statistical methods the reconstruction of positron emission tomography (PET) images can be improved by high-resolution anatomical information obtained from magnetic resonance (MR) images. The authors implemented two approaches that utilize MR data for PET reconstruction. The anatomical MR information is modeled as a priori distribution of the PET image and combined with the distribution of the measured PET data to generate the a posteriori function from which the expectation maximization (EM)-type algorithm with a maximum a posteriori (MAP) estimator is derived. One algorithm (Markov-GEM) uses a Gibbs function to model interactions between neighboring pixels within the anatomical regions. The other (Gauss-EM) applies a Gauss function with the same mean for all pixels in a given anatomical region. A basic assumption of these methods is that the radioactivity is homogeneously distributed inside anatomical regions. Simulated and phantom data are investigated under the following aspects: count density, object size, missing anatomical information, and misregistration of the anatomical information. Compared with the maximum likelihood-expectation maximization (ML-EM) algorithm the results of both algorithms show a large reduction of noise with a better delineation of borders. Of the two algorithms tested, the Gauss-EM method is superior in noise reduction (up to 50%). Regarding incorrect a priori information the Gauss-EM algorithm is very sensitive, whereas the Markov-GEM algorithm proved to be stable with a small change of recovery coefficients between 0.5 and 3%.

Expectation Maximization Reconstruction of Positron Emission Tomography Images Using Anatomical Magnetic Resonance Information B. Lipinski, H. Herzog,* E. Rota Kops, W. Oberschelp, and H. W. M¨ uller-G¨

Abstract: Using statistical methods the reconstruction of positron emission tomography (PET) images can be improved by high-resolution anatomical information obtained from magnetic resonance (MR) images. We implemented two approaches that utilize MR data for PET reconstruction. The anatomical MR information is modeled as a priori distribution of the PET image and combined with the distribution of the measured PET data to generate the a posteriori function from which the expectation maximization (EM)-type algorithm with a maximum a posteriori (MAP) estimator is derived. One algorithm (Markov-GEM) uses a Gibbs function to model interactions between neighboring pixels within the anatomical regions. The other (Gauss-EM) applies a Gauss function with the same mean for all pixels in a given anatomical region. A basic assumption of these methods is that the radioactivity is homogeneously distributed inside anatomical regions. Simulated and phantom data are investigated under the following aspects: count density, object size, missing anatomical information, and misregistration of the anatomical information. Compared with the maximum likelihood-expectation maximization (ML-EM) algorithm the results of both algorithms show a large reduction of noise with a better delineation of borders. Of the two algorithms tested, the Gauss-EM method is superior in noise reduction (up to 50%). Regarding incorrect a priori information the Gauss-EM algorithm is very sensitive, whereas the Markov-GEM algorithm proved to be stable with a small change of recovery coefficients between 0.5 and 3%.

Inverse halftoning via MAP estimation

Abstract: There has been a tremendous amount of research in the area of image halftoning, where the goal has been to find the most visually accurate representation given a limited palette of gray levels (often just two, black and white). This paper focuses on the inverse problem, that of finding efficient techniques for reconstructing high-quality continuous-tone images from their halftoned versions. The proposed algorithms are based on a maximum a posteriori (MAP) estimation criteria using a Markov random field (MRF) model for the prior image distribution. Image estimates obtained with the proposed model accurately reconstruct both the smooth regions of the image and the discontinuities along image edges. Algorithms are developed and example gray-level reconstructions are presented generated from both dithered and error-diffused halftone originals. Application of the technique to the problems of rescreening and the processing of halftone images are shown.

Optimal speckle reduction for the product model in multilook polarimetric SAR imagery and the Wishart distribution

Abstract: Several optimal techniques exist to reduce speckle effects on polarimetric data, e.g. the Linear Minimum Mean Square Error (LMMSE) vector filter for multilook detected data or optimum summations such as the Polarimetric Whitening Filter (PWF) for one look complex data. Among other drawbacks, these standard methods do not preserve full polarimetric data, or they do not use the a priori texture distribution, or they are restricted to one look data. In the simplified case of data satisfying the so-called "product model", new optimal techniques are described in this paper that are able to reduce speckle effects on multilook data, while preserving fully polarimetric information and texture variations. This "product model" is valid when the scene texture has a large scale of variation and is polarization independent, for instance in K-distributed clutter. Under this assumption, the measured covariance matrix (multilook data) is the product of a scalar random variable /spl mu/ (the texture) and the covariance matrix C/sub zh/ of an equivalent Gaussian homogeneous surface. C/sub zh/ is the mean covariance matrix and contains the polarimetric information. A PWF for multilook complex data (MPWF) is proposed and is shown to be related to optimal statistical estimators of the texture (Maximum Likelihood, Maximum A Posteriori, MMSE...) when the complex Wishart distribution is used. The ML estimation of C/sub zh/ for textured areas is given and the adaptive filters based on these new tools are described. The results indicate a large speckle reduction. Moreover, the mean values of polarimetric features such as the magnitude and the phase of the HH-VV complex degree of coherence are preserved.

Nonlinear techniques for the joint estimation of cochannel signals

Abstract: Cochannel interference occurs when two or more signals overlap in frequency and are present concurrently. Unlike in spread-spectrum multiple-access systems where the different users necessarily share the same channel, cochannel interference is a severe hindrance to frequency- and time-division multiple-access communications, and is typically minimized by interference rejection/suppression techniques. Rather than using interference suppression, we are interested in the joint estimation of the information-bearing narrow-band cochannel signals. Novel joint estimators are proposed that employ a single-input demodulator with oversampling to compensate for timing uncertainties. Assuming finite impulse-response channel characteristics, maximum likelihood (ML) and maximum a posteriori (MAP) criteria are used to derive cochannel detectors of varying complexities and degrees of performance. In particular, a (suboptimal) two-stage joint MAP symbol detector (JMAPSD) is introduced that has a lower complexity than the single-stage estimators while accruing only a marginal loss in error-rate performance at high signal-to-interference ratios. Assuming only reliable estimates of the primary and secondary signal powers, a blind adaptive JMAPSD algorithm for a priori unknown channels is also derived. The performance of these nonlinear joint estimation algorithms is studied through example computer simulations for two cochannel sources.

Noise analysis of MAP - EM algorithms for emission tomography

Abstract: The ability to theoretically model the propagation of photon noise through PET and SPECT tomographic reconstruction algorithms is crucial in evaluating the reconstructed image quality as a function of parameters of the algorithm. In a previous approach for the important case of the iterative ML-EM (maximum-likelihood-expectation-maximization) algorithm, judicious linearizations were used to model theoretically the propagation of a mean image and a covariance matrix from one iteration to the next. Our analysis extends this approach to the case of MAP (maximum a posteriori)-EM algorithms, where the EM approach incorporates prior terms. We analyse in detail two cases: a MAP-EM algorithm incorporating an independent gamma prior, and a one-step-late (OSL) version of a MAP-EM algorithm incorporating a multivariate Gaussian prior, for which familiar smoothing priors are special cases. To validate our theoretical analyses, we use a Monte Carlo methodology to compare, at each iteration, theoretical estimates of mean and covariance with sample estimates, and show that the theory works well in practical situations where the noise and bias in the reconstructed images do not assume extreme values.

Bayesian Methods for Finite Population Sampling

Abstract: Bayesian Foundations Notation Sufficiency The Sufficiency and Likelihood Principles A Bayesian Example Posterior Linearity Overview A Noninfromative Bayesian Approach A Binomial Example A Characterization of Admissibility Admissibility of the Sample Mean Set Estimation The Polya Urn The Polya Posterior Simulating the Polya Posterior Some Examples Extensions of the Polya Posterior Prior Information Using an Auxiliary Variable Stratification and Prior Information Choosing between Experiments Nonresponse Some Nonparametric Problems Linear Interpolation Empirical Bayes Estimation Introduction Stepwise Bayes Estimators Estimation of Stratum Means Robust Estimation of Stratum Means Multistage Sampling Auxiliary Information Nested Error Regression Models Hierarchical Bayes Estimation Introduction Stepwise Bayes Estimators Estimation of Stratum Means Auxiliary Information I Auxiliary Information II

A scheme for approximating probabilistic inference

Abstract: This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable explanation, belief updating and finding the maximum a posteriori hypothesis. We identify regions of completeness and provide preliminary empirical evaluation on randomly generated networks.

Multimodality Bayesian algorithm for image reconstruction in positron emission tomography: a tissue composition model

Abstract: The use of anatomical information to improve the quality of reconstructed images in positron emission tomography (PET) has been extensively studied. A common strategy has been to include spatial smoothing within boundaries defined from the anatomical data. The authors present an alternative method for the incorporation of anatomical information into PET image reconstruction, in which they use segmented magnetic resonance (MR) images to assign tissue composition to PET image pixels. The authors model the image as a sum of activities for each tissue type, weighted by the assigned tissue composition. The reconstruction is performed as a maximum a posteriori (MAP) estimation of the activities of each tissue type. Two prior functions, defined for tissue-type activities, are considered. The algorithm is tested in realistic simulations employing a full physical model of the PET scanner.

Structural MAP speaker adaptation using hierarchical priors

Abstract: Most adaptation methods for speech recognition using hidden Markov models fall into two categories; one is the Bayesian approach, where prior distributions for the model parameters are assumed, and the other is the transformation-based approach, where a pre-determined simple transformation form is employed to modify the model parameters. It is known that the former is better when the amount of data for adaptation is large, while the latter is better when the amount of data is small. In this paper, we propose a new approach, the structural maximum a posteriori (SMAP) approach, in which hierarchical priors are introduced to combine the two approaches above. Experimental results showed that SMAP achieved a better recognition accuracy than the two individual approaches for both small and large amounts of adaptation data.

Hyperparameter selection for self-organizing maps

Abstract: The self-organizing map (SOM) algorithm for finite data is derived as an approximate maximum a posteriori estimation algorithm for a gaussian mixture model with a gaussian smoothing prior, which is equivalent to a generalized deformable model (GDM). For this model, objective criteria for selecting hyperparameters are obtained on the basis of empirical Bayesian estimation and cross-validation, which are representative model selection methods. The properties of these criteria are compared by simulation experiments. These experiments show that the cross-validation methods favor more complex structures than the expected log likelihood supports, which is a measure of compatibility between a model and data distribution. On the other hand, the empirical Bayesian methods have the opposite bias.

Quantization of memoryless and Gauss-Markov sources over binary Markov channels

Abstract: Joint source-channel coding for stationary memoryless and Gauss-Markov sources and binary Markov channels is considered. The channel is an additive-noise channel where the noise process is an Mth-order Markov chain. Two joint source-channel coding schemes are considered. The first is a channel-optimized vector quantizer-optimized for both source and channel. The second scheme consists of a scalar quantizer and a maximum a posteriori detector. In this scheme, it is assumed that the scalar quantizer output has residual redundancy that can be exploited by the maximum a posteriori detector to combat the correlated channel noise. These two schemes are then compared against two schemes which use channel interleaving. Numerical results show that the proposed schemes outperform the interleaving schemes. For very noisy channels with high noise correlation, gains of 4-5 dB in signal-to-noise ratio are possible.

Efficient superresolution restoration algorithms using maximum a posteriori estimations with application to fluorescence microscopy

Abstract: We present efficient algorithms for image restoration by using the maximum a posteriori (MAP) method. Assuming Gaussian or Poisson statistics for the noise and either a Gaussian or an entropy prior distribution for the image, corresponding functionals are formulated and minimized to produce MAP estimations. Efficient algorithms are presented for finding the minimum of these functionals in the presence of nonnegativity and support constraints. Performance was tested by using simulated three-dimensional (3-D) imaging with a fluorescence confocal laser scanning microscope. Results are compared with those from two existing algorithms for superresolution in fluorescence imaging. An example is given of the restoration of a 3-D confocal image of a biological specimen.

Task adaptation using MAP estimation in N-gram language modeling

Abstract: Describes a method of task adaptation in N-gram language modeling for accurately estimating the N-gram statistics from the small amount of data of the target task. Assuming a task-independent N-gram to be a-priori knowledge, the N-gram is adapted to a target task by MAP (maximum a-posteriori probability) estimation. Experimental results showed that the perplexities of the task-adapted models were 15% (trigram) and 24% (bigram) lower than those of the task-independent model, and that the perplexity reduction of the adaptation went up to a maximum of 39% when the amount of text data in the adapted task was very small.

Image segmentation using multiresolution wavelet analysis and expectation‐maximization (EM) algorithm for digital mammography

Abstract: This article presents a novel algorithm for image seg- been developed for classification purposes. In addition, many mentation via the use of the multiresolution wavelet analysis and the authors have discovered significant advantages in the use of the expectation maximization (EM) algorithm. The development of a multiresolution concept ( 4,5 ) . Brazkovic and Neskovic presented multiresolution wavelet feature extraction scheme is based on the the Gaussian pyramid and fuzzy linking method for the adaptive Gaussian Markov random field (GMRF) assumption in mammo- detection of cancerous changes in mammograms (6). graphic image modeling. Mammographic images are hierarchically Recently, as a result of cross-fertilization of innovative ideas decomposed into different resolutions. In general, larger breast le- from image processing, spatial statistics, and statistical physics, sions are characterized by coarser resolutions, whereas higher resolu- a significant amount of research activity on image modeling and tions show finer and more detailed anatomical structures. These hier- archical variations in the anatomical features displayed by multiresolu- segmentation has also been concentrated on the two-dimensional tion decomposition are further quantified through the application of ( 2D ) Markov random field ( MRF ) . Although many of the poten- the Gaussian Markov random field. Because of its uniqueness in local- tials of MRF had been envisioned by the early works of Levy ity, adaptive features based on the nonstationary assumption of (7), McCormick and Jayaramamrhy (8), and Abend et al. (9), GMRF are defined for each pixel of the mammogram. Fibroadenomas exploitation of the powers of the MRF was not possible until are then segmented via the fuzzy C-means algorithm using these significant recent advances occurred in the appropriate mathemat- localized features. Subsequently, the segmentation results are further ical and computational tools. Chellappa and Kashyap (10 ) suc- enhanced via the introduction of a maximum a posteriori (MAP) seg- cessfully applied the noncausal autoregressive ( NCAR ) model mentation estimation scheme based on the Bayesian learning para-

The calibration of P-values, posterior Bayes factors and the AIC from the posterior distribution of the likelihood

Abstract: The posterior distribution of the likelihood is used to interpret the evidential meaning of P-values, posterior Bayes factors and Akaike‘s information criterion when comparing point null hypotheses with composite alternatives. Asymptotic arguments lead to simple re-calibrations of these criteria in terms of posterior tail probabilities of the likelihood ratio. (’Prior‘) Bayes factors cannot be calibrated in this way as they are model-specific.

A hybrid algorithm for speaker adaptation using MAP transformation and adaptation

Abstract: We present a hybrid algorithm for adapting a set of speaker-independent hidden Markov models (HMMs) to a new speaker based on a combination of maximum a posteriori (MAP) parameter transformation and adaptation. The algorithm is developed by first transforming clusters of HMM parameters through a class of transformation functions. Then, the transformed HMM parameters are further smoothed via Bayesian adaptation. The proposed transformation/adaptation process can be iterated for any given amount of adaptation data, and it converges rapidly in terms of likelihood improvement. The algorithm also gives a better speech recognition performance than that obtained using transformation or adaptation alone for almost any practical amount of adaptation data.

Comparison of a genetic algorithm and simulated annealing in an application to statistical image reconstruction

Abstract: Genetic algorithms (GAs) are adaptive search techniques designed to find near-optimal solutions of large scale optimization problems with multiple local maxima. Standard versions of the GA are defined for objective functions which depend on a vector of binary variables. The problem of finding the maximum a posteriori (MAP) estimate of a binary image in Bayesian image analysis appears to be well suited to a GA as images have a natural binary representation and the posterior image probability is a multi-modal objective function. We use the numerical optimization problem posed in MAP image estimation as a test-bed on which to compare GAs with simulated annealing (SA), another all-purpose global optimization method. Our conclusions are that the GAs we have applied perform poorly, even after adaptation to this problem. This is somewhat unexpected, given the widespread claims of GAs‘ effectiveness, but it is in keeping with work by Jennison and Sheehan (1995) which suggests that GAs are not adept at handling problems involving a great many variables of roughly equal influence. We reach more positive conclusions concerning the use of the GA‘s crossover operation in recombining near-optimal solutions obtained by other methods. We propose a hybrid algorithm in which crossover is used to combine subsections of image reconstructions obtained using SA and we show that this algorithm is more effective and efficient than SA or a GA individually.

A Markov random field approach to Bayesian speaker adaptation

Abstract: Speaker adaptation through Bayesian learning methodology is studied in this paper. In order to utilize the cross allophone correlations, a Markov random field (MRF) model is proposed as the joint prior distribution of the mean vectors of the allophones. Neighborhoods are defined as pairs of parameters between which strong correlations have been observed previously. Maximum a posteriori estimates of the mean vectors are obtained through an iterative optimization technique that converges to the global maximum of the posterior distribution. This process is similar to a recursive prediction of the parameters, where at each iteration each parameter is estimated by a weighted sum of two terms, the first predicted by the neighbors and the second by the samples. Further Bayesian smoothing of the output distributions is carried out by utilizing some simplifications on the functional forms of the marginal posterior distributions. The proposed method is fast, consuming only a few CPU minutes for processing hundreds of sentences from a new speaker on an IBM RS6000 Model 580 system. Experimental results show rapid improvement of recognition accuracy.

On maneuvering target tracking via the PMHT

Abstract: This paper presents an iterative off-line optimal state estimation algorithm, which yields the maximum a posteriori (MAP) state trajectory estimate of the state sequence of a target maneuvering in clutter. The problem is formulated as a jump Markov linear system and the expectation maximization algorithm is used to compute the state sequence estimate. The proposed algorithm optimally combines a hidden Markov model and a Kalman smoother to yield the MAP target state sequence estimate. The algorithm proposed uses probabilistic multi-hypothesis tracking (PMHT) techniques for tracking a single maneuvering target in clutter. Previous applications of the PMHT technique have addressed the problem of tracking multiple non-maneuvering targets. These techniques are extended to address the problem of optimal (in a MAP sense) tracking of a maneuvering target in clutter.

Model based speech pause detection

Abstract: This paper presents two new algorithms for robust speech pause detection (SPD) in noise. Our approach was to formulate SPD into a statistical decision theory problem for the optimal detection of noise-only segments, using the framework of model-based speech enhancement (MBSE). The advantages of this approach are that it performs well in high noise conditions, all necessary information is available in MBSE, and no other features are required to be computed. The first algorithm is based on a maximum a posteriori probability (MAP) test and the second is based on a Neyman-Pearson test. These tests are seen to make use of the spectral distance between the input vector and the composite spectral prototypes of the speech and noise models, as well as the probabilistic framework of the hidden Markov model. The algorithms are evaluated and shown to perform well against different types of noise at various SNRs.