Bayesian mixture models of variable dimension for image segmentation

Bayesian pooling versus sequential integration of small preclinical trials: a comparison within linear and nonlinear modeling frameworks

Bayesian sequential integration is an appealing approach in drug development, as it allows to recursively update posterior distributions as soon as new data become available, thus considerably reducing the computation time. However, preclinical trials are often characterized by small sample sizes, which may affect the estimation process during the first integration steps, particularly when complex PK-PD models are used. In this case, sequential integration would not be practicable, and trials should be pooled together. This work is aimed at comparing simple Bayesian pooling with sequential integration through a simulation study. The two techniques are compared under several scenarios using linear as well as nonlinear models. The results of our simulation study encourage the use of Bayesian sequential integration with linear models. However, in the case of nonlinear models several caveats arise. This paper outlines some important recommendations and precautions in that respect.

A Heavy Tailed Expectation Maximization Hidden Markov Random Field Model with Applications to Segmentation of MRI

A wide range of segmentation approaches assumes that intensity histograms extracted from magnetic resonance images (MRI) have a distribution for each brain tissue that can be modeled by a Gaussian distribution or a mixture of them. Nevertheless, intensity histograms of White Matter and Gray Matter are not symmetric and they exhibit heavy tails. In this work, we present a hidden Markov random field model with expectation maximization (EM-HMRF) modeling the components using the α-stable distribution. The proposed model is a generalization of the widely used EM-HMRF algorithm with Gaussian distributions. We test the α-stable EM-HMRF model in synthetic data and brain MRI data. The proposed methodology presents two main advantages: Firstly, it is more robust to outliers. Secondly, we obtain similar results than using Gaussian when the Gaussian assumption holds. This approach is able to model the spatial dependence between neighboring voxels in tomographic brain MRI.

A unified Bayesian hierarchical model for MRI tissue classification

Various works have used magnetic resonance imaging (MRI) tissue classification extensively to study a number of neurological and psychiatric disorders. Various noise characteristics and other artifacts make this classification a challenging task. Instead of splitting the procedure into different steps, we extend a previous work to develop a unified Bayesian hierarchical model, which addresses both the partial volume effect and intensity non-uniformity, the two major acquisition artifacts, simultaneously. We adopted a normal mixture model with the means and variances depending on the tissue types of voxels to model the observed intensity values. We modeled the relationship among the components of the index vector of tissue types by a hidden Markov model, which captures the spatial similarity of voxels. Furthermore, we addressed the partial volume effect by construction of a higher resolution image in which each voxel is divided into subvoxels. Finally, We achieved the bias field correction by using a Gaussian Markov random field model with a band precision matrix designed in light of image filtering. Sparse matrix methods and parallel computations based on conditional independence are exploited to improve the speed of the Markov chain Monte Carlo simulation. The unified model provides more accurate tissue classification results for both simulated and real data sets.

Parameterization of the distribution of white and grey matter in MRI using the α-stable distribution

This work presents a study of the distribution of the grey matter (GM) and white matter (WM) in brain magnetic resonance imaging (MRI). The distribution of GM and WM is characterized using a mixture of α-stable distributions. A Bayesian α-stable mixture model for histogram data is presented and unknown parameters are sampled using the Metropolis-Hastings algorithm. The proposed methodology is tested in 18 real images from the MRI brain segmentation repository. The GM and WM distributions are accurately estimated. The α-stable distribution mixture model presented in this paper can be used as previous step in more complex MRI segmentation procedures using spatial information. Furthermore, due to the fact that the α-stable distribution is a generalization of the Gaussian distribution, the proposed methodology can be applied instead of the Gaussian mixture model, which is widely used in segmentation of brain MRI in the literature.

Spatial based expectation maximizing (EM)

BACKGROUND

Expectation maximizing (EM) is one of the common approaches for image segmentation.

METHODS

an improvement of the EM algorithm is proposed and its effectiveness for MRI brain image segmentation is investigated. In order to improve EM performance, the proposed algorithms incorporates neighbourhood information into the clustering process. At first, average image is obtained as neighbourhood information and then it is incorporated in clustering process. Also, as an option, user-interaction is used to improve segmentation results. Simulated and real MR volumes are used to compare the efficiency of the proposed improvement with the existing neighbourhood based extension for EM and FCM.

RESULTS

the findings show that the proposed algorithm produces higher similarity index.

CONCLUSIONS

experiments demonstrate the effectiveness of the proposed algorithm in compare to other existing algorithms on various noise levels.

A Bayesian multilevel model for fMRI data analysis

Bayesian approaches have been proposed by several functional magnetic resonance imaging (fMRI) researchers in order to overcome the fundamental limitations of the popular statistical parametric mapping method. However, the difficulties associated with subjective prior elicitation have prevented the widespread adoption of the Bayesian methodology by the neuroimaging community. In this paper, we present a Bayesian multilevel model for the analysis of brain fMRI data. The main idea is to consider that all the estimated group effects (fMRI activation patterns) are exchangeable. This means that all the collected voxel time series are considered manifestations of a few common underlying phenomena. In contradistinction to other Bayesian approaches, we think of the estimated activations as multivariate random draws from the same distribution without imposing specific prior spatial and/or temporal information for the interaction between voxels. Instead, a two-stage empirical Bayes prior approach is used to relate voxel regression equations through correlations between the regression coefficient vectors. The adaptive shrinkage properties of the Bayesian multilevel methodology are exploited to deal with spatial variations, and noise outliers. The characteristics of the proposed model are evaluated by considering its application to two real data sets.