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PubMed1997

Estimating the bias field of MR images.

We propose a modification of Wells et al. technique for bias field estimation and segmentation of magnetic resonance (MR) images. We show that replacing the class other, which includes all tissue not modeled explicitly by Gaussians with small variance, by a uniform probability density, and amending the expectation-maximization (EM) algorithm appropriately, gives significantly better results. We next consider the estimation and filtering of high-frequency information in MR images, comprising noise, intertissue boundaries, and within tissue microstructures. We conclude that post-filtering is preferable to the prefiltering that has been proposed previously. We observe that the performance of any segmentation algorithm, in particular that of Wells et al. (and our refinements of it) is affected substantially by the number and selection of the tissue classes that are modeled explicitly, the corresponding defining parameters and, critically, the spatial distribution of tissues in the image. We present an initial exploration to choose automatically the number of classes and the associated parameters that give the best output. This requires us to define what is meant by "best output" and for this we propose the application of minimum entropy. The methods developed have been implemented and are illustrated throughout on simulated and real data (brain and breast MR).

Algorithms↗

PubMed1997

The design of an animal PET: flexible geometry for achieving optimal spatial resolution or high sensitivity.

We present the design of a positron emission tomograph (PET) with flexible geometry dedicated to in vivo studies of small animals (TierPET). The scanner uses two pairs of detectors. Each detector consists of 400 small individual yttrium aluminum perovskite (YAP) scintillator crystals of dimensions 2 x 2 x 15 mm3, optically isolated and glued together, which are coupled to position-sensitive photomultiplier tubes (PSPMT's). The detector modules can be moved in a radial direction so that the detector-to-detector spacing can be varied. Special hardware has been built for coincidence detection, position detection, and real-time data acquisition, which is performed by a PC. The single-event data are transferred to workstations where the radioactivity distribution is reconstructed. The dimensions of the crystals and the detector layout are the result of extensive simulations which are described in this report, taking into account sensitivity, spatial resolution and additional parameters like parallax error or scatter effects. For the three-dimensional (3-D) reconstruction a genuine 3-D expectation-maximization (EM)-algorithm which can include the characteristics of the detector system has been implemented. The reconstruction software is flexible and matches the different detector configurations. The main advantage of the proposed animal PET scanner is its high flexibility, allowing the realization of various detector-system configurations. By changing the detector-to-detector spacing, the system is capable of either providing good spatial resolution or high sensitivity for dynamic studies of pharmacokinetics.

Algorithms↗

PubMed1998

Robust parameter estimation of intensity distributions for brain magnetic resonance images.

This paper presents two new methods for robust parameter estimation of mixtures in the context of magnetic resonance (MR) data segmentation. The head is constituted of different types of tissue that can be modeled by a finite mixture of multivariate Gaussian distributions. Our goal is to estimate accurately the statistics of desired tissues in presence of other ones of lesser interest. These latter can be considered as outliers and can severely bias the estimates of the former. For this purpose, we introduce a first method, which is an extension of the expectation-maximization (EM) algorithm, that estimates parameters of Gaussian mixtures but incorporates an outlier rejection scheme which allows to compute the properties of the desired tissues in presence of atypical data. The second method is based on genetic algorithms and is well suited for estimating the parameters of mixtures of different kind of distributions. We use this property by adding a uniform distribution to the Gaussian mixture for modeling the outliers. The proposed genetic algorithm can efficiently estimate the parameters of this extended mixture for various initial settings. Also, by changing the minimization criterion, estimates of the parameters can be obtained by histogram fitting which considerably reduces the computational cost. Experiments on synthetic and real MR data show that accurate estimates of the gray and white matters parameters are computed.

Adolescent↗

PubMed2000

Reconstruction of two- and three-dimensional images from synthetic-collimator data.

A novel SPECT collimation method, termed the synthetic collimator, is proposed. The synthetic collimator employs a multiple-pinhole aperture and a high-resolution detector. The problem of multiplexing, normally associated with multiple pinholes, is reduced by obtaining projections at a number of pinhole-detector distances. Projections with little multiplexing are collected at small pinhole-detector distances and high-resolution projections are collected at greater pinhole-detector distances. These projections are then reconstructed using the ML-EM algorithm. It is demonstrated through computer simulations that the synthetic collimator has superior resolution properties to a high-resolution parallel-beam (HRPB) collimator and a specially built ultra-high-resolution parallel-beam (UHRPB) collimator designed for our 0.38-mm pixel CdZnTe detectors. It is also shown that reconstructing images in three dimensions is superior to reconstructing them in two dimensions. The advantages of a high-resolution synthetic collimator over the parallel-hole collimators are apparently reduced in the presence of statistical noise. However, a high-sensitivity synthetic collimator was designed which again shows superior properties to the parallel-hole collimators. Finally, it is demonstrated that, for the cases studied, high-resolution detectors are necessary for the proper functionality of the synthetic collimator.

Algorithms↗

PubMedDate not supplied

Analyzing gene expression time-courses.

Measuring gene expression over time can provide important insights into basic cellular processes. Identifying groups of genes with similar expression time-courses is a crucial first step in the analysis. As biologically relevant groups frequently overlap, due to genes having several distinct roles in those cellular processes, this is a difficult problem for classical clustering methods. We use a mixture model to circumvent this principal problem, with hidden Markov models (HMMs) as effective and flexible components. We show that the ensuing estimation problem can be addressed with additional labeled data-partially supervised learning of mixtures-through a modification of the Expectation-Maximization (EM) algorithm. Good starting points for the mixture estimation are obtained through a modification to Bayesian model merging, which allows us to learn a collection of initial HMMs. We infer groups from mixtures with a simple information-theoretic decoding heuristic, which quantifies the level of ambiguity in group assignment. The effectiveness is shown with high-quality annotation data. As the HMMs we propose capture asynchronous behavior by design, the groups we find are also asynchronous. Synchronous subgroups are obtained from a novel algorithm based on Viterbi paths. We show the suitability of our HMM mixture approach on biological and simulated data and through the favorable comparison with previous approaches. A software implementing the method is freely available under the GPL from http://ghmm.org/gql.

Algorithms↗

PubMed2006

Varying complexity in tree-structured image distribution models.

Probabilistic models of image statistics underlie many approaches in image analysis and processing. An important class of such models have variables whose dependency graph is a tree. If the hidden variables take values on a finite set, most computations with the model can be performed exactly, including the likelihood calculation, training with the EM algorithm, etc. Crouse et al. developed one such model, the hidden Markov tree (HMT). They took particular care to limit the complexity of their model. We argue that it is beneficial to allow more complex tree-structured models, describe the use of information theoretic penalties to choose the model complexity, and present experimental results to support these proposals. For these experiments, we use what we call the hierarchical image probability (HIP) model. The differences between the HIP and the HMT models include the use of multivariate Gaussians to model the distributions of local vectors of wavelet coefficients and the use of different numbers of hidden states at each resolution. We demonstrate the broad utility of image distributions by applying the HIP model to classification, synthesis, and compression, across a variety of image types, namely, electrooptical, synthetic aperture radar, and mammograms (digitized X-rays). In all cases, we compare with the HMT.

Algorithms↗

PubMed2003

Mixtures of general linear models for functional neuroimaging.

We set out a new general framework for making inferences from neuroimaging data, which includes a standard approach to neuroimaging analysis, statistical parametric mapping (SPM), as a special case. The model offers numerous conceptual and statistical advantages that derive from analyzing data at the "cluster level" rather than the "voxel level" and from explicit modeling of the shape and position of clusters of activation. This provides a natural and principled way to pool data from nearby voxels for parameter and variance-component estimation. The model can also be viewed as performing a spatio-temporal cluster analysis. The parameters of the model are estimated using an expectation maximization (EM) algorithm.

Acoustic Stimulation↗

PubMed2005

Direct reconstruction of kinetic parameter images from dynamic PET data.

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

Algorithms↗

PubMed2005

A spatially constrained mixture model for image segmentation.

Gaussian mixture models (GMMs) constitute a well-known type of probabilistic neural networks. One of their many successful applications is in image segmentation, where spatially constrained mixture models have been trained using the expectation-maximization (EM) framework. In this letter, we elaborate on this method and propose a new methodology for the M-step of the EM algorithm that is based on a novel constrained optimization formulation. Numerical experiments using simulated images illustrate the superior performance of our method in terms of the attained maximum value of the objective function and segmentation accuracy compared to previous implementations of this approach.

Neural Networks, Computer↗

PubMed2006

An incremental training method for the probabilistic RBF network.

The probabilistic radial basis function (PRBF) network constitutes a probabilistic version of the RBF network for classification that extends the typical mixture model approach to classification by allowing the sharing of mixture components among all classes. The typical learning method of PRBF for a classification task employs the expectation-maximization (EM) algorithm and depends strongly on the initial parameter values. In this paper, we propose a technique for incremental training of the PRBF network for classification. The proposed algorithm starts with a single component and incrementally adds more components at appropriate positions in the data space. The addition of a new component is based on criteria for detecting a region in the data space that is crucial for the classification task. After the addition of all components, the algorithm splits every component of the network into subcomponents, each one corresponding to a different class. Experimental results using several well-known classification data sets indicate that the incremental method provides solutions of superior classification performance compared to the hierarchical PRBF training method. We also conducted comparative experiments with the support vector machines method and present the obtained results along with a qualitative comparison of the two approaches.

Algorithms↗

PubMed2005

Speedup OS-EM Image Reconstruction by PC Graphics Card Technologies for Quantitative SPECT with Varying Focal-Length Fan-Beam Collimation.

In the paper, we present a new hardware acceleration method to speedup the ordered-subsets expectation-maximization (OS-EM) algorithm for quantitative SPECT (single photon emission computed tomography) image reconstruction with varying focal-length fan-beam (VFF) collimation. By utilizing the geometrical symmetry of VFF point-spread function (PSF), compensation for object-specific attenuation and system-specific PSF are accelerated using currently available PC video/graphics card technologies. A ten-fold acceleration of quantitative SPECT reconstruction is achieved.

Journal Article↗

PubMed2004

A Bayesian approach to joint feature selection and classifier design.

This paper adopts a Bayesian approach to simultaneously learn both an optimal nonlinear classifier and a subset of predictor variables (or features) that are most relevant to the classification task. The approach uses heavy-tailed priors to promote sparsity in the utilization of both basis functions and features; these priors act as regularizers for the likelihood function that rewards good classification on the training data. We derive an expectation-maximization (EM) algorithm to efficiently compute a maximum a posteriori (MAP) point estimate of the various parameters. The algorithm is an extension of recent state-of-the-art sparse Bayesian classifiers, which in turn can be seen as Bayesian counterparts of support vector machines. Experimental comparisons using kernel classifiers demonstrate both parsimonious feature selection and excellent classification accuracy on a range of synthetic and benchmark data sets.

Algorithms↗

PubMed2005

Clustering ensembles: models of consensus and weak partitions.

Clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph-based, combinatorial, or statistical perspectives. This study extends previous research on clustering ensembles in several respects. First, we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem. Second, we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings. A combined partition is found as a solution to the corresponding maximum-likelihood problem using the EM algorithm. Third, we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition. Finally, we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits. A simple explanatory model is offered for the behavior of combinations of such weak clustering components. Combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions. We also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus. Experimental results demonstrate the effectiveness of the proposed methods on several real-world data sets.

Algorithms↗

PubMed2003

Likelihood inference for exchangeable binary data with varying cluster sizes.

This article investigates maximum likelihood estimation with saturated and unsaturated models for correlated exchangeable binary data, when a sample of independent clusters of varying sizes is available. We discuss various parameterizations of these models, and propose using the EM algorithm to obtain maximum likelihood estimates. The methodology is illustrated by applications to a study of familial disease aggregation and to the design of a proposed group randomized cancer prevention trial.

Algorithms↗

PubMed1999

Applying the Cox proportional hazards model when the change time of a binary time-varying covariate is interval censored.

This paper develops methodology for estimation of the effect of a binary time-varying covariate on failure times when the change time of the covariate is interval censored. The motivating example is a study of cytomegalovirus (CMV) disease in patients with human immunodeficiency virus (HIV) disease. We are interested in determining whether CMV shedding predicts an increased hazard for developing active CMV disease. Since a clinical screening test is needed to detect CMV shedding, the time that shedding begins is only known to lie in an interval bounded by the patient's last negative and first positive tests. In a Cox proportional hazards model with a time-varying covariate for CMV shedding, the partial likelihood depends on the covariate status of every individual in the risk set at each failure time. Due to interval censoring, this is not always known. To solve this problem, we use a Monte Carlo EM algorithm with a Gibbs sampler embedded in the E-step. We generate multiple completed data sets by drawing imputed exact shedding times based on the joint likelihood of the shedding times and event times under the Cox model. The method is evaluated using a simulation study and is applied to the data set described above.

AIDS-Related Opportunistic Infections↗

PubMed1999

Dual screening.

We discuss the problem of screening a general population for characteristics such as HIV or drug use. Our main approach is Bayesian, which allows for the incorporation of prior information about parameters. In the particular problem we consider, there is currently no information in the data for estimating the sensitivity of the screening test, and consequently, the prevalence of the characteristic among screened negatives cannot be estimated from the collected data alone. Our inferences are straightforward to obtain using Gibbs sampling techniques, and they are valid for large or small samples and for arbitrary prevalence or accuracy of screening tests. We also develop the maximum-likelihood approach using the EM algorithm.

AIDS Serodiagnosis↗

PubMed1999

Modeling tumor onset and multiplicity using transition models with latent variables.

We describe a method for modeling carcinogenicity from animal studies where the data consist of counts of the number of tumors present over time. The research is motivated by applications to transgenic rodent studies, which have emerged as an alternative to chronic bioassays for screening possible carcinogens. In transgenic mouse studies, the endpoint of interest is frequently skin papilloma, with weekly examinations determining how many papillomas each animal has at a particular point in time. It is assumed that each animal has two unobservable latent variables at each time point. The first indicates whether or not the tumors are in a multiplying state and the second is the potential number of additional tumors if the tumors are in a multiplying state. The product of these variables follows a zero-inflated Poisson distribution, and the EM algorithm can be used to maximize the observed-data pseudo-likelihood, based on the latent variables. A generalized estimating equations robust variance estimator adjusts for dependency among outcomes within individual animals. The method is applied to testing for a dose-related trend in both tumor incidence and multiplicity in carcinogenicity studies.

Algorithms↗

PubMed1999

Estimating regression parameters and degree of dependence for multivariate failure time data.

Multivariate failure time data are frequently encountered in longitudinal studies when subjects may experience several events or when there is a grouping of individuals into a cluster. To take into account the dependence of the failure times within the unit (the individual or the cluster) as well as censoring, two multivariate generalizations of the Cox proportional hazards model are commonly used. The marginal hazard model is used when the purpose is to estimate mean regression parameters, while the frailty model is retained when the purpose is to assess the degree of dependence within the unit. We propose a new approach based on the combination of the two aforementioned models to estimate both these quantities. This two-step estimation procedure is quicker and more simple to implement than the EM algorithm used in frailty models estimation. Simulation results are provided to illustrate robustness, consistency, and large-sample properties of estimators. Finally, this method is exemplified on a diabetic retinopathy study in order to assess the effect of photocoagulation in delaying the onset of blindness as well as the dependence between the two eyes blindness times of a patient.

Biometry↗