fMRI data analysis with nonstationary noise models: a Bayesian approach

The assumption of noise stationarity in the functional magnetic resonance imaging (fMRI) data analysis may lead to the loss of crucial dynamic features of the data and thus result in inaccurate activation detection. In this paper, a Bayesian approach is proposed to analyze the fMRI data with two nonstationary noise models (the time-varying variance noise model and the fractional noise model). The covariance matrices of the time-varying variance noise and the fractional noise after wavelet transform are diagonal matrices. This property is investigated under the Bayesian framework. The Bayesian estimator not only gives an accurate estimate of the weights in general linear model, but also provides posterior probability of activation in a voxel and, hence, avoids the limitations (i.e., using only hypothesis testing) in the classical methods. The performance of the proposed Bayesian methods (under the assumption of different noise models) are compared with the ordinary least squares (OLS) and the weighted least squares (WLS) methods. Results from the simulation studies validate the superiority of the proposed approach to the OLS and WLS methods considering the complex noise structures in the fMRI data.     

A Bayesian network modeling approach for cross media analysis

Existing methods for the semantic analysis of multimedia, although effective for single-medium scenarios, are inherently flawed in cases where knowledge is spread over different media types. In this work we implement a cross media analysis scheme that takes advantage of both visual and textual information for detecting high-level concepts. The novel aspect of this scheme is the definition and use of a conceptual space where information originating from heterogeneous media types can be meaningfully combined and facilitate analysis decisions. More specifically, our contribution is on proposing a modeling approach for Bayesian Networks that defines this conceptual space and allows evidence originating from the domain knowledge, the application context and different content modalities to support or disproof a certain hypothesis. Using this scheme we have performed experiments on a set of 162 compound documents taken from the domain of car manufacturing industry and 118 581 video shots taken from the TRECVID2010 competition. The obtained results have shown that the proposed modeling approach exploits the complementary effect of evidence extracted across different media and delivers performance improvements compared to the single-medium cases. Moreover, by comparing the performance of the proposed approach with an approach using Support Vector Machines (SVM), we have verified that in a cross media setting the use of generative rather than discriminative models are more suited, mainly due to their ability to smoothly incorporate explicit knowledge and learn from a few examples.     

Bayesian approach with hidden Markov modeling and mean field approximation for hyperspectral data analysis

The main problems in hyperspectral image analysis are spectral classification, segmentation, and data reduction. In this paper, we propose a Bayesian estimation approach which gives a joint solution for these problems. The problem is modeled as a blind sources separation (BSS). The data are M hyperspectral images and the sources are K < M images which are composed of compact homogeneous regions and have mutually disjoint supports. The set of all these regions cover the total surface of the observed scene. To insure these properties, we propose a hierarchical Markov model for the sources with a common hidden classification field which is modeled via a Potts-Markov field. The joint Bayesian estimation of the hidden variable, sources, and the mixing matrix of the BSS gives a solution for all three problems: spectra classification, segmentation, and data reduction of hyperspectral images. The mean field approximation (MFA) algorithm for the posterior laws is proposed for the effective Bayesian computation. Finally, some results of the application of the proposed methods on simulated and real data are given to illustrate the performance of the proposed method compared to other classical methods, such as PCA and ICA.     

A model-based mixture-supervised classification approach in hyperspectral data analysis

It is well known that there is a strong relation between class definition precision and classification accuracy in pattern classification applications. In hyperspectral data analysis, usually classes of interest contain one or more components and may not be well represented by a single Gaussian density function. In this paper, a model-based mixture classifier, which uses mixture models to characterize class densities, is discussed. However, a key outstanding problem of this approach is how to choose the number of components and determine their parameters for such models in practice, and to do so in the face of limited training sets where estimation error becomes a significant factor. The proposed classifier estimates the number of subclasses and class statistics simultaneously by choosing the best model. The structure of class covariances is also addressed through a model-based covariance estimation technique introduced in this paper.     

Application of Bayesian inference to fMRI data analysis

The methods of Bayesian statistics are applied to the analysis of fMRI data. Three specific models are examined. The first is the familiar linear model with white Gaussian noise. In this section, the Jeffreys' Rule for noninformative prior distributions is stated and it is shown how the posterior distribution may be used to infer activation in individual pixels. Next, linear time-invariant (LTI) systems are introduced as an example of statistical models with nonlinear parameters. It is shown that the Bayesian approach can lead to quite complex bimodal distributions of the parameters when the specific case of a delta function response with a spatially varying delay is analyzed. Finally, a linear model with auto-regressive noise is discussed as an alternative to that with uncorrelated white Gaussian noise. The analysis isolates those pixels that have significant temporal correlation under the model. It is shown that the number of pixels that have a significantly large auto-regression parameter is dependent on the terms used to account for confounding effects.     

Mixed-Weibull parameter estimation for burn-in data using the Bayesian approach

A Bayesian approach is presented for both grouped and ungrouped burn-in test data, to come up with the posterior parameters of the bimodal mixed-Weibull distribution. The concepts of belonging probabilities and fractional ranks are introduced for this approach. A numerical comparison is made by conducting the Kolmogorov-Smirnov goodness-of-fit test on the parameter estimates obtained by Jensen's graphical method, by the Bayesian approach using the conventional separation plotting method and by the Bayesian approach using the fractional rank plotting method. It turns out that the Bayesian approach with the fractional rank plotting method yields the best results.     

A Bayesian approach to geometric subspace estimation

This paper presents a geometric approach to estimating subspaces as elements of the complex Grassmann-manifold, with each subspace represented by its unique, complex projection matrix. Variation between the subspaces is modeled by rotating their projection matrices via the action of unitary matrices [elements of the unitary group U(n)]. Subspace estimation or tracking then corresponds to inferences on U(n). Taking a Bayesian approach, a posterior density is derived on U(n), and certain expectations under this posterior are empirically generated. For the choice of the Hilbert-Schmidt norm on U(n), to define estimation errors, an optimal MMSE estimator is derived. It is shown that this estimator achieves a lower bound on the expected squared errors associated with all possible estimators. The estimator and the bound are computed using (Metropolis-adjusted) Langevin's-diffusion algorithm for sampling from the posterior. For use in subspace tracking, a prior model on subspace rotation, that utilizes Newtonian dynamics, is suggested     

A Bayesian approach to robust adaptive beamforming

An adaptive beamformer that is robust to uncertainty in source direction-of-arrival (DOA) is derived using a Bayesian approach. The DOA is assumed to be a discrete random variable with a known a priori probability density function (PDF) that reflects the level of uncertainty in the source DOA. The resulting beamformer is a weighted sum of minimum variance distortionless response (MVDR) beamformers pointed at a set of candidate DOAs, where the relative contribution of each MVDR beamformer is determined from the a posteriori PDF of the DOA conditioned on previously observed data. A simple approximation to the a posteriori PDF results in a straightforward implementation. Performance of the approximate Bayesian beamformer is compared with linearly constrained minimum variance (LCMV) beamformers and data-driven approaches that attempt to estimate signal characteristics or the steering vector from the data     

A sparse Bayesian method for determination of flexible design matrix for fMRI data analysis

The construction of a design matrix is critical to the accurate detection of activation regions of the brain in functional magnetic resonance imaging (fMRI). The design matrix should be flexible to capture the unknown slowly varying drifts as well as robust enough to avoid overfitting. In this paper, a sparse Bayesian learning method is proposed to determine a suitable design matrix for fMRI data analysis. Based on a generalized linear model, this learning method lets the data itself determine the form of the regressors in the design matrix. It automatically finds those regressors that are relevant to the generation of the fMRI data and discards the others that are irrelevant. The proposed approach integrates the advantages of currently employed methods of fMRI data analysis (the model-driven and the data-driven methods). Results from the simulation studies clearly reveal the superiority of the proposed scheme to the conventional t-test method of fMRI data analysis.     

A Bayesian approach for classification of Markov sources

A Bayesian approach for classification of Markov sources whose parameters are not explicitly known is developed and studied. A universal classifier is derived and shown to achieve, within a constant factor, the minimum error probability in a Bayesian sense. The proposed classifier is based on sequential estimation of the parameters of the sources, and it is closely related to earlier proposed universal tests under the Neyman-Pearson criterion     

A different approach to the analysis of data in life-tests of laser diodes

A different reading of the available I–V curves is proposed for laser diodes whose characteristics display some degradation. In particular, the usual monitoring of the optical power P and of the threshold current I_th is complemented by the inspection of two more parameters, which separately or jointly contribute to the general variation of I_th. These two parameters are related to the simplest laser model, made of an ideal diode that is voltage-clamped under operating conditions, and are completely defined by those same standard measurements that lead to evaluate I_th. A different definition of the failure modes, and a deeper insight in the possible failure mechanisms are derived. Combined voltage and optical power monitoring during constant-current life-tests is also proposed as a more discriminating measurement than usually considered.     

A Bayesian classification approach with application to speechrecognition

A Bayesian approach to classification of parametric information sources whose statistics are not explicitly given is studied and applied to recognition of speech signals based upon Markov modeling. A classifier based on generalized likelihood ratios, which depends only on the available training and testing data, is developed and shown to be optimal in the sense of achieving the highest asymptotic exponential rate of decay of the error probability. The proposed approach is compared to the standard classification approach used in speech recognition, in which the parameters for the sources are first estimated from the given training data, and then the maximum a posteriori decision rule is applied using the estimated statistics     

A Bayesian approach for stochastic white matter tractography

White matter fiber bundles in the human brain can be located by tracing the local water diffusion in diffusion weighted magnetic resonance imaging (MRI) images. In this paper, a novel Bayesian modeling approach for white matter tractography is presented. The uncertainty associated with estimated white matter fiber paths is investigated, and a method for calculating the probability of a connection between two areas in the brain is introduced. The main merits of the presented methodology are its simple implementation and its ability to handle noise in a theoretically justified way. Theory for estimating global connectivity is also presented, as well as a theorem that facilitates the estimation of the parameters in a constrained tensor model of the local water diffusion profile.     

A variational approach for Bayesian blind image deconvolution

In this paper, the blind image deconvolution (BID) problem is addressed using the Bayesian framework. In order to solve for the proposed Bayesian model, we present a new methodology based on a variational approximation, which has been recently introduced for several machine learning problems, and can be viewed as a generalization of the expectation maximization (EM) algorithm. This methodology reaps all the benefits of a "full Bayesian model" while bypassing some of its difficulties. We present three algorithms that solve the proposed Bayesian problem in closed form and can be implemented in the discrete Fourier domain. This makes them very cost effective even for very large images. We demonstrate with numerical experiments that these algorithms yield promising improvements as compared to previous BID algorithms. Furthermore, the proposed methodology is quite general with potential application to other Bayesian models for this and other imaging problems.     

A multidimensional classification approach for the automated analysis of flow cytometry data

We describe an automated multidimensional approach for the analysis of flow cytometry data based on pattern classification. Flow cytometry is a widely used technique both for research and clinical purposes where it has become essential for the diagnosis and follow up of a wide spectrum of diseases, such as HIV-infection and neoplastic disorders. Flow cytometry data sets are composed of quite a large number of observations that can be viewed as elements of a n-dimensional space. The aim of the analysis of such data files is typically to classify groups of cellular events as specific populations with biological meaning. Despite significant improvements in data acquisition capabilities of flow cytometers, data analysis is still based on bi-dimensional strategies which were defined a long time ago. These are strongly dependent on the expertise of an expert operator, this approach being relatively subjective and potentially leading to unreliable results. Automated analysis of flow cytometry data is an essential step to improve reproducibility of the results. The proposed automated analysis was implemented on peripherial blood lymphocyte subsets from 307 samples stained and prepared in an identical way and it was capable of identifying all cell subsets present in each sample studied that could also be detected in the same data files by an expert operator. A highly significant correlation was found between the results obtained by an expert operator using a conventional manual method of analysis and those obtained using the implemented automated approach.     

A computer-aided approach to the structural analysis and modification of a large circulatory system model

The purpose of this study is to show an approach to making an intelligent support system for understanding and modifying a large circulatory system model using techniques of system analysis. Structural analysis makes it possible to visualize hierarchies of Coleman's circulatory model Human. Two techniques are successively applied for structural analysis, model reduction and graph analysis by interpretative structural modeling (ISM). First, the analysis for model reduction removes input-output relations with an input-output gain less than a given threshold, and second, the ISM technique applied to the reduced model of Human provides hierarchical directed graphs. The proposed approach: 1) enables visualization of a hierarchy graph of cause and effect relations of the large circulatory model, 2) suggests control and diagnostic information to the model by tracing back a path in the hierarchy, and 3) allows the user to modify the circulatory model. The efficiency and performance of the proposed approach demonstrates technical indications of success in analyzing and justifying experimental evidences with the online help of the system.     

Bayesian approach with the maximum entropy principle in image reconstruction from microwave scattered field data

Microwave imaging is of great interest in medical applications owing to its high sensitivity with respect to dielectric properties. It allows detection of very small inhomogeneities. The image reconstruction employing the microwave inverse scattering consists of reconstructing the image of an object from the scattered field measured behind the object. This reconstruction runs up against the nonuniqueness of the solution of the inverse scattering problem. The authors propose to solve the ill-posed inverse problem by a statistical regularization method based on the Bayesian maximum a posteriori estimation where the principle of maximum entropy is used for assigning the a priori laws. The results obtained demonstrate the power and potential of this method in image reconstruction.     

A joint multicontext and multiscale approach to Bayesian imagesegmentation

In this paper, a joint multicontext and multiscale (JMCMS) approach to Bayesian image segmentation is proposed. In addition to the multiscale framework, the JMCMS applies multiple context models to jointly use their distinct advantages, and we use a heuristic multistage, problem-solving technique to estimate sequential maximum a posteriori of the JMCMS. The segmentation results on both synthetic mosaics and remotely sensed images show that the proposed JMCMS improves the classification accuracy, and in particular, boundary localization and detection over the methods using a single context at comparable computational complexity     

A Bayesian approach to image expansion for improved definition

Accurate image expansion is important in many areas of image analysis. Common methods of expansion, such as linear and spline techniques, tend to smooth the image data at edge regions. This paper introduces a method for nonlinear image expansion which preserves the discontinuities of the original image, producing an expanded image with improved definition. The maximum a posteriori (MAP) estimation techniques that are proposed for noise-free and noisy images result in the optimization of convex functionals. The expanded images produced from these methods will be shown to be aesthetically and quantitatively superior to images expanded by the standard methods of replication, linear interpolation, and cubic B-spline expansion.