Andreas Galka

• Kiel University

In this article, a particular approach to deriving recursive state estimators for linear state space models is generalised, namely the weighted least-squares approach introduced by Duncan and Horn in 1972, for the case of the two noise processes arising in such models being cross-correlated; in this context, the fact that in the available literatur...

This paper proposes a class of algorithms for analyzing event count time series, based on state space modeling and Kalman filtering. While the dynamics of the state space model is kept Gaussian and linear, a nonlinear observation function is chosen. In order to estimate the states, an iterated extended Kalman filter is employed. Positive definitene...

In this study, we present a thorough comparison of the performance of four different bootstrap methods for assessing the significance of causal analysis in time series data. For this purpose, multivariate simulated data are generated by a linear feedback system. The methods investigated are uncorrelated Phase Randomization Bootstrap (uPRB), which g...

In this study, we meticulously compared the practical performance of four bootstrap methods for assessing the significance of causal analysis in time series data, recognizing that their evaluation has not been sufficiently conducted in the field. The methods investigated were uncorrelated Phase Randomization Bootstrap (uPRB), which generates surrog...

In this paper we study hydroacoustic time series by parametric predictive modelling, using linear state space models. The aim is to detect, separate and characterise sound components emitted by complex sources such as ships, marine mammals, explosions, etc. The models are fitted to the data by Kalman filtering and maximisation of the likelihood, us...

Background and objective: The human brain displays rich and complex patterns of interaction within and among brain networks that involve both cortical and subcortical brain regions. Due to the limited spatial resolution of surface electroencephalography (EEG), EEG source imaging is used to reconstruct brain sources and investigate their spatial and...

Abstract This paper discusses the fitting of linear state space models to given multivariate time series in the presence of constraints imposed on the four main parameter matrices of these models. Constraints arise partly from the assumption that the models have a block-diagonal structure, with each block corresponding to an ARMA process, that allo...

Non-linear State space model , Cox-Stuart trend test

In this paper a nonlinear filtering algorithm for count time series is developed that takes the non-negativity of the data into account and preserves positive definiteness of the covariance matrices of the model. For this purpose, a recently proposed variant of Kalman Filtering based on Singular Value Decomposition is incorporated into Iterative Ex...

Magnetic nanoparticles (MNPs) are a hot topic in the field of medical life sciences, as they are highly relevant in diagnostic applications. In this regard, a large variety of novel imaging methods for MNP in biological systems have been invented. In this proof-of-concept study, a new and novel technique is explored, called Magnetic Particle Mappin...

Objective Multifocal epileptic activity is an unfavourable feature of a number of epileptic syndromes (Lennox-Gastaut syndrome, West syndrome, severe focal epilepsies) which suggests an overall vulnerability of the brain to pathological synchronization. However, the mechanisms of multifocal activity are insufficiently understood. This explorative s...

the aim of this proof-of-concept work was to apply the spatiotemporal Kalman filter (STKF) algorithm to magnetocardiographic (MCG) recordings of the heart. Due to the lack of standardized software and pipelines for MCG source imaging, we needed to construct a pipeline for MCG forward modeling before we could apply the STKF method. In the forward mo...

This paper proposes an objective methodology for the analysis of epileptic seizure count time series by developing a non-linear state space model. An iterative extended Kalman filter (IEKF) is employed for the estimation of the states of the non-linear state space model. In order to improve convergence of the IEKF, the recently proposed Levenberg-...

The clinical routine of non-invasive electroencephalography (EEG) is usually performed with 8-40 electrodes, especially in long-term monitoring, infants or emergency care. There is a need in clinical and scientific brain imaging to develop inverse solution methods that can reconstruct brain sources from these low-density EEG recordings. In this pro...

The reconstruction of brain sources from non-invasive electroencephalography (EEG) or magnetoencephalography (MEG) via source imaging can be distorted by information redundancy in case of high-resolution recordings. Dimensionality reduction approaches such as spatial projection may be used to alleviate this problem. In this proof-of-principle paper...

Independent component analysis (ICA) is an approved method for (e.g., muscle) artifact removal in electroencephalography (EEG). But, as it creates only \(m \le n\) components from n signals, it may fail to clearly separate the artifacts. In order to keep the strengths of ICA and overcome its limitations, we extend ICA by state-space modeling (SSM),...

In this paper, we present a method for investigating the coupling of structure-borne sound (SBS) and underwater sound (UWS) of ships based on a decomposition in optimal frequency bands. The coupling is modeled by a linear regression model for sequences of spectral power, integrated over frequency intervals and moving time windows. As part of this a...

Recently, interest has been growing to understand the underlying dynamic directional relationship between simultaneously activated regions of the brain during motor task performance. Such directionality analysis (or effective connectivity analysis), based on non-invasive electrophysiological (electroencephalography-EEG) and hemodynamic (functional...

This authoritative work provides an in-depth treatment of state space methods, with a range of applications in neural and clinical data. Advanced and state-of-the-art research topics are detailed, including topics in state space analyses, maximum likelihood methods, variational Bayes, sequential Monte Carlo, Markov chain Monte Carlo, nonparametric...

The discretization of the brain and the definition of the Laplacian matrix influence the results of methods based on spatial and spatio-temporal smoothness, since the Laplacian operator is used to define the smoothness based on the neighborhood of each grid point. In this paper, the results of low resolution electromagnetic tomography (LORETA) and...

The assumption of spatial-smoothness is often used to solve the bioelectric inverse problem during electroencephalographic (EEG) source imaging, e.g., in low resolution electromagnetic tomography (LORETA). Since the EEG data show a temporal structure, the combination of the temporal-smoothness and the spatial-smoothness constraints may improve the...

We propose an approach for the analysis of epileptic seizure count time series within a state space framework. Time-dependent dosages of several simultaneously administered anticonvulsants are included as external inputs. The method aims at distinguishing which temporal correlations in the data are due to the medications, and which correspond to an...

Source localization of an epileptic seizure is becoming an important diagnostic tool in pre-surgical evaluation of epileptic patients. However, for localizing the epileptogenic zone precisely, the epileptic activity needs to be isolated from other activities that are not related to the epileptic source. In this study, we aim at an investigation of...

The traditional financial econometric studies presume the underlying data generating processes (DGP) of the time series observations to be linear and stochastic. These assumptions were taken face value for a long time; however, recent advances in dynamical systems theory and algorithms have enabled researchers to observe complicated dynamics of tim...

To increase the reliability for the non-invasive determination of the irritative zone in presurgical epilepsy diagnosis, we introduce here a new experimental and methodological source analysis pipeline that combines the complementary information in EEG and MEG, and apply it to data from a patient, suffering from refractory focal epilepsy. Skull con...

One of the important prerequisites for successful social interaction is the willingness of each individual to cooperate socially. Using the ultimatum game, several studies have demonstrated that the process of decision-making to cooperate or to defeat in interaction with a partner is associated with activation of the dorsolateral prefrontal cortex...

We perform a systematic comparison between different algorithms for solving the Blind Signal Separation problem. In particular, we compare five well-known algorithms for Independent Component Analysis (ICA) with a recently proposed algorithm based on linear state space modeling (IC–LSS). The comparison is based on simulated mixtures of six source s...

Brain activity can be measured using different modalities. Since most of the modalities tend to complement each other, it seems promising to measure them simultaneously. In to be presented research, the data recorded from Functional Magnetic Resonance Imaging (fMRI) and Near Infrared Spectroscopy (NIRS), simultaneously, are subjected to causality a...

Simultaneous recording of electroencephalogram (EEG) and electromyogram (EMG) with magnetic resonance imaging (MRI) provides great potential for studying human brain activity with high temporal and spatial resolution. But, due to the MRI, the recorded signals are contaminated with artifacts. The correction of these artifacts is important to use the...

Electroencephalogram (EEG) is a useful tool for brain research. However, during Deep-Brain Stimulation (DBS), there are large artifacts that obscure the physiological EEG signals. In this paper, we aim at suppressing the DBS artifacts by means of a time-frequency-domain filter. As a pre-processing step, Empirical-Mode Decomposition (EMD) is applied...

The fusion of data from multiple neuroimaging modalities may improve the temporal and spatial resolution of non-invasive brain imaging. In this paper, we present a novel method for the fusion of simultaneously recorded electroencephalograms (EEG) and magnetoencephalograms (MEG) within the framework of source analysis. This method represents an exte...

We propose a novel state space modelling approach to removing scanner-related artifacts from electroencephalograms recorded inside MR scanners. For this purpose, dynamical templates for the actual brain activity and the ballistocardiogram are obtained from a short piece of data recorded without fMRI scanning; dynamical templates for the scanner art...

Electroencephalographic (EEG) recordings are sometimes contaminated by spurious periodic components picked up from the power-supply equipment. The removal of these components presents a demanding problem because the current techniques do not suppress the artifact efficiently: Either the artifact is only partly eliminated, allowing some residual con...

Directionality analysis of signals originating from different parts of brain during motor tasks has gained a lot of interest. Since brain activity can be recorded over time, methods of time series analysis can be applied to medical time series as well. Granger Causality is a method to find a causal relationship between time series. Such causality c...

In this paper, we aim at suppressing the muscle artifacts present in electroencephalographic (EEG) signals with a technique based on a combination of Independent Component Analysis (ICA) and State-Space Modeling (SSM). The novel algorithm uses ICA to provide an initial model for SSM which is further optimized by the maximimum-likelihood approach. T...

Akaike's Noise Contribution Ratio (NCR) has been used for the analysis of causality of two-variable settings of biological time series in Neuroscience. In contrast to the conventional correlation definition, this methodology is able to detect the direction of the influence between two variables. However, if a third series intervention is taken...

Using simultaneous recordings of EEG and functional MRI (EEG-fMRI) in patients with focal epilepsy, recent studies have revealed insufficient sensitivity and a lack of correspondence between epileptic EEG foci and activation patterns in some patients. In this study of children with focal epilepsy, we explore whether sleep-specific activity (sleep s...

In this paper, we design an algorithm for decomposing multivariate electroencephalographic (EEG) time series into independent components, based on Independent-Component Analysis (ICA) and State-Space Modeling (SSM). We aim at combining the strong aspects of both methods: ICA provides an initial model for SSM which is then further optimized by maxim...

The problem of extracting a set of independent components from given multivariatetime series data under the assumption of linear instantaneous mixing can be addressedwithin a Kalman filtering framework. For this purpose, we introduce a new class ofstate space models, the Independent Components State Space Model (IC - SSM). Theresulting algorithm ha...

Decomposition of multivariate time series data into independent source components forms an important part of preprocessing and analysis of time-resolved data in neuroscience. We briefly review the available tools for this purpose, such as Factor Analysis (FA) and Independent Component Analysis (ICA), then we show how linear state space modelling, a...

For the purpose of statistical characterization of the spatio-temporal correlation structure of brain functioning from high-dimensional fMRI time series, we introduce an innovation approach. This is based on whitening the data by the Nearest-Neighbors AutoRegressive model with external inputs (NN-ARx). Correlations between the resulting innovations...

The analysis of time series obtained by functional magnetic resonance imaging (fMRI) may be approached by fitting predictive parametric models, such as nearest-neighbor autoregressive models with exogeneous input (NNARX). As a part of the modeling procedure, it is possible to apply instantaneous linear transformations to the data. Spatial smoothing...

In a thorough study, the multitaper (MTM) and the extended continuous wavelet-transform (CWT) coherence-analysis methods were compared in terms of there application in determining the dynamics from the electroencephalogram (EEG) and electromyogram (EMG) signals of patients with Parkinsonian tremor. The main aim of the study in a biological point of...

In this chapter we discuss a comprehensive framework for decomposing nonstationary time-series into a set of constituent processes. Our methodology is based on autoregressive moving-average (ARMA) modeling and on state-space modeling. For the purpose of modeling nonstationary phenomena, such as sudden phase transitions in dynamical behavior, we emp...

Electroencephalographic (EEG) source localization is an important tool for noninvasive study of brain dynamics, due to its ability to probe neural activity more directly, with better temporal resolution than other imaging modalities. One promising technique for solving the EEG inverse problem is Kalman filtering, because it provides a natural frame...

We discuss a model for the dynamics of the primary current density vector field within the grey matter of human brain. The model is based on a linear damped wave equation, driven by a stochastic term. By employing a realistically shaped average brain model and an estimate of the matrix which maps the primary currents distributed over grey matter to...

We present a new approach to modelling non-stationarity in EEG time series by a generalized state space approach. A given time series can be decomposed into a set of noise-driven processes, each corresponding to a different frequency band. Non-stationarity is modelled by allowing the variances of the driving noises to change with time, depending on...

We suggest a procedure to identify those parts of the spectrum of the equal-time correlation matrix C where relevant information about correlations of a multivariate time series is induced. Using an ensemble average over each of the distances between eigenvalues, all nearest-neighbor distributions can be calculated individually. We present numerica...

We address the issue of inferring the connectivity structure of spatially extended dynamical systems by estimation of mutual information between pairs of sites. The well-known problems resulting from correlations within and between the time series are addressed by explicit temporal and spatial modelling steps which aim at approximately removing all...

We propose a method based on the equal-time correlation matrix as a sensitive detector for phase-shape correlations in multivariate data sets. The key point of the method is that changes of the degree of synchronization between time series provoke level repulsions between eigenstates at both edges of the spectrum of the correlation matrix. Conseque...

The problem of estimating unobserved states of spatially extended dynamical systems poses an inverse problem, which can be solved approximately by a recently developed variant of Kalman filtering; in order to provide the model of the dynamics with more flexibility with respect to space and time, we suggest to combine the concept of GARCH modelling...

We present a new approach for estimating solutions of the dynamical inverse problem of EEG generation. In contrast to previous approaches, we reinterpret this problem as a filtering problem in a state space framework; for the purpose of its solution, we propose a new extension of Kalman filtering to the case of spatiotemporal dynamics. The temporal...

The purpose of this study is to propose and investigate a new approach for discriminating between focal and non-focal hemispheres in intractable temporal lobe epilepsy, based on applying multivariate time series analysis to the discharge-free background brain activity observed in nocturnal electrocorticogram (ECoG) time series. Five unilateral foca...

In the dynamical inverse problem of electroencephalogram (EEG) generation where a specific dynamics for the electrical current distribution is assumed, we can impose general spatiotemporal constraints onto the solution by casting the problem into a state space representation and assuming a specific class of parametric models for the dynamics. The A...

We consider the problem of detecting and quantifying nonstationary structure in time series from high-dimensional dynamical systems. This problem is relevant in particular for EEG monitoring, e.g. for the prediction of epileptic seizures, but also for practical data analysis in many other fields. Three groups of measures of nonstationarity are disc...

We use the theory of nonlinear dynamical systems to measure the complexity of currency markets by estimating the correlation dimension of the returns of the Dollar/Pound and Dollar/Yen daily exchange rates (the spot rates). We test the significance of the re-sults by comparing them to correlation dimension estimates for surrogate time series, i.e....

We investigate the structure of dynamical correlations on reconstructed attractors which were obtained by time-delay embedding of periodic, quasi-periodic and chaotic time series. Within the specific sampling of the invariant density by a finite number of vectors which results from embedding, we identify two separate levels of sampling, correspondi...

We address the issue of testing for nonlinearity in time series from continuous dynamics and propose a quantitative measure for nonlinearity which is based on discrete parametric modelling. The well-known problems of modelling continuous dynamical systems by discrete models are addressed by a subsampling approach. This measure should preferably be...

We present a very simple approach to the generation of interspike intervals which reduces univariate EEG time series to pure phase information. By this transformation the effects of certain artifacts and other low-frequency noise components can be greatly reduced, and the data sets which are submitted to further analysis become much smaller. In ord...

We compare two algorithms for the numerical estimation of the correlation dimension from a finite set of vectors: the “classical” algorithm of Grassberger and Procaccia (GPA) and the recently proposed algorithm of Judd (JA). Data set size requirements and their relations to systematic and statistical errors of the estimates are investigated. It is...

As a new framework in EEG study we propose 'dynamic' inverse prob- lem where dynamical constraints for a solution is considered. This is an extension of instantaneous inverse problem which many researchers have been studying to obtain a solution with good localization ability. We intro- duce a model for solving the problem, what we call "Dynamic LO...

x1(t),...,xN(t) , t = 1,...,T where N denotes the number of channels and T the number of sampling times. A linear state space (linSS) model for x(t) can be defined by an observation equation x(t) = Cs(t) + (t) where C denotes the observation matrix, s(t) s1(t),...,sM(t) the source components (or factors), M the dimension of s(t) and (t) measurement...

In this paper we study the application of classical methods for dynamical modelling of time series to the task of decomposing multivariate time series into approximately independent source components, a task that has traditionally been addressed by Factor Analysis (FA) and more recently by Independent Component Analysis (ICA). Based on maximum-like...

Kiel, Univ., Diss., 2000 (Nicht für den Austausch).