Vangelis P. Oikonomou

A Kalman filter based methodology for EEG spike enhancement

In this work, we present a methodology for spike enhancement in electroencephalographic (EEG) recordings. Our approach takes advantage of the non-stationarity nature of the EEG signal using a time-varying autoregressive model. The time-varying coefficients of autoregressive model are estimated using the Kalman filter. The results show considerable improvement in signal-to-noise ratio and significant reduction of the number of false positives.

A Sparse and Spatially Constrained Generative Regression Model for fMRI Data Analysis

In this study, we present an advanced Bayesian framework for the analysis of functional magnetic resonance imaging (fMRI) data that simultaneously employs both spatial and sparse properties. The basic building block of our method is the general linear regression model that constitutes a well-known probabilistic approach. By treating regression coefficients as random variables, we can apply an enhanced Gibbs distribution function that captures spatial constrains and at the same time allows sparse representation of fMRI time series. The proposed scheme is described as a maximum a posteriori approach, where the known expectation maximization algorithm is applied offering closed-form update equations for the model parameters. We have demonstrated that our method produces improved performance and functional activation detection capabilities in both simulated data and real applications.

Bayesian Methods for fMRI Time-Series Analysis Using a Nonstationary Model for the Noise

In this paper, the Bayesian framework is used for the analysis of functional MRI (fMRI) data. Two algorithms are proposed to deal with the nonstationarity of the noise. The first algorithm is based on the temporal analysis of the data, while the second algorithm is based on the spatiotemporal analysis. Both algorithms estimate the variance of the noise across the images and the voxels. The first algorithm is based on the generalized linear model (GLM), while the second algorithm is based on a spatiotemporal version of it. In the GLM, an extended design matrix is used to deal with the presence of the drift in the fMRI time series. To estimate the regression parameters of the GLM as well as the variance components of the noise, the variational Bayesian (VB) methodology is employed. The use of the VB methodology results in an iterative algorithm, where the estimation of the regression coefficients and the estimation of variance components of the noise, across images and voxels, are interchanged in an elegant and fully automated way. The performance of the proposed algorithms (under the assumption of different noise models) is compared with the weighted least-squares (WLSs) method. Results using simulated and real data indicate the superiority of the proposed approach compared to the WLS method, thus taking into account the complex noise structure of the fMRI time series.

An Adaptive Regression Mixture Model for fMRI Cluster Analysis

Functional magnetic resonance imaging (fMRI) has become one of the most important techniques for studying the human brain in action. A common problem in fMRI analysis is the detection of activated brain regions in response to an experimental task. In this work we propose a novel clustering approach for addressing this issue using an adaptive regression mixture model. The main contribution of our method is the employment of both spatial and sparse properties over the body of the mixture model. Thus, the clustering approach is converted into a maximum a posteriori estimation approach, where the expectation-maximization algorithm is applied for model training. Special care is also given to estimate the kernel scalar parameter per cluster of the design matrix by presenting a multi-kernel scheme. In addition an incremental training procedure is presented so as to make the approach independent on the initialization of the model parameters. The latter also allows us to introduce an efficient stopping criterion of the process for determining the optimum brain activation area. To assess the effectiveness of our method, we have conducted experiments with simulated and real fMRI data, where we have demonstrated its ability to produce improved performance and functional activation detection capabilities.

The Use of Kalman Filter in Biomedical Signal Processing

The Kalman Filter (KF) is a powerful tool in the analysis of the evolution of a dynamical model in time. The filter provides with a flexible manner to obtain recursive estimation of the parameters, which are optimal in the mean square error sense. The properties of KF along with the simplicity of the derived equations make it valuable in the analysis of signals. In this chapter an overview of the Kalman Filter, its properties and its applications is presented. More specifically, we focus on the application of Kalman Filter in the Electroencephalogram (EEG) processing, addressing extensions of Kalman Filter such as the Kalman Smoother (KS) in the time varying autoregressive (TVAR) model. The model can be written in a state – space form and the employment of KF provides with an estimation of the AR parameters which can be used for the estimation of the non – stationary signal. It is also demonstrated how these parameters can be used as input features of the signal in a clustering approach. The Kalman Filter is an estimator with interesting properties like optimality in the Minimum Mean Square Error (MMSE). After its discovery in 1960 (Kalman, 1960), this estimator has been used in many fields of engineering such as control theory, communication systems, speech processing, biomedical signal processing, etc. An analogous estimator has been proposed for the smoothing problem (Rauch et al., 1963), which includes three different types of smoothers, namely fixed-lag, fixed-point and fixed interval (Anderson & Moore, 1979; Brown, 1983). In this chapter we address the fixed interval smoother. The difference between the two estimators, the Kalman Filter and the Kalman Smoother, it is related on how they use the observations to perform estimation. The Kalman Filter uses only the past and the present observations to perform estimation, while the Kalman Smoother uses also the future observations for the estimation. This means that the Kalman Filter is used for on - line processing while the Kalman Smoother for batch processing. The derivations of these two estimators is presented in (Kay, 1993; Grewal & Andrews, 2001; Haykin, 2001). Both estimators are recursive in nature. This means that the estimate of the present state is updated using the previous state only and not the entire past states. The Kalman Filter is not only an estimator but also a learning method (Grewal & Andrews, 2001; Bishop, 2006). The observations are used to learn the states of the model. The Kalman Filter is also a computational tool and some problems may exist due to the finite precision arithmetic of the computers.

A sparse variational Bayesian approach for fMRI data analysis

The aim of this work is to propose a new approach for the determination of the design matrix in fMRI experiments. The design matrix embodies all available knowledge about experimentally controlled factors and potential confounds. This knowledge is expressed through the regressors of the design matrix. However, in a particular fMRI time series some of those regressors may not be present. In order to take into account this prior information a Bayesian approach based on hierarchical prior, which expresses the sparsity of the design matrix, is used over the parameters of the generalized linear model. The proposed method automatically prunes the columns of the design matrix which are irrelevant to the generation of data. The evaluation of the proposed approach on simulated and real experiments have shown higher performance compared to the conventional t-test approach.

Resting state fMRI analysis using a spatial regression mixture model

Functional MRI (fMRI) is one of the most important techniques to study the human brain. A relatively new problem to the analysis of fMRI data is the identification of brain networks when the brain is at rest i.e. no external stimulus is applied to the subject. In this work a method to find the Resting State Networks (RSNs), using fMRI time series, is proposed. To achieve that our method uses the Regression Mixtures Models (RMMs). RMMs are mixture models specifically design to cluster time series. Furthermore, our method takes into account the spatial correlations of fMRI data by using a new functional for the responsibilities of the mixture. Experimental results have showed the usefullness of the proposed approach compared to other methods of the field such as the k-means algorithm.

Steady state visual evoked potential detection using Subclass Marginal Fisher Analysis

Recently, SSVEP detection from EEG signals has attracted the interest of the research community, leading to a number of well-tailored methods, such as Canonical Correlation Analysis (CCA) and a number of variants. Despite their effectiveness, due to their strong dependence on the correct calculation of correlations, these methods may prove to be inadequate in front of potential deficiency in the number of channels used, the number of available trials or the duration of the acquired signals. In this paper, we propose the use of Subclass Marginal Fisher Analysis (SMFA) in order to overcome such problems. SMFA has the power to effectively learn discriminative features of poor signals, and this advantage is expected to offer the appropriate robustness needed in order to handle such deficiencies. In this context, we pinpoint the qualitative advantages of SMFA, and through a series of experiments we prove its superiority over the state-of-the-art in detecting SSVEPs from EEG signals acquired with limited resources.

A Comparison Study on EEG Signal Processing Techniques Using Motor Imagery EEG Data

Brain-computer interfaces (BCIs) have been gaining momentum in making human-computer interaction more natural, especially for people with neuro-muscular disabilities. Among the existing solutions the systems relying on electroencephalograms (EEG) occupy the most prominent place due to their non-invasiveness. In this work, we provide a review of various existing techniques for the identification of motor imagery (MI) tasks. More specifically, we perform a comparison between Common Spatial Patterns (CSP) related features and features based on Power Spectral Density (PSD) techniques. Furthermore, for the identification of MI tasks, two well-known classifiers are used, the Linear Discriminant Analysis (LDA) and the Support Vector Machines (SVM). Our results confirm that PSD features demonstrate the most consistent robustness and effectiveness in extracting patterns for accurately discriminating between left and right MI tasks.

A sparse linear model for the analysis of fMRI data with non stationary noise

In this work we present a bayesian approach for the estimation of the regression parameters in the analysis of fMRI data when the noise is non - stationary. The proposed approach is based on the Variational Bayesian (VB) Methodology and the Generalized Linear Model (GLM). The VB methodology permits the use of prior distributions over the parameters of the noise. This results to a very elegant approach to estimate the time varying variance of the noise and to overcome the problem of over - parameterization which is present in the estimation procedure. The proposed approach is compared to the Weighted Least Square (WLS) and is evaluated using simulated and real fMRI time series. The proposed approach shows better performance than WLS.