Simon G. Fabri

Review on solving the inverse problem in EEG source analysis

In this primer, we give a review of the inverse problem for EEG source localization. This is intended for the researchers new in the field to get insight in the state-of-the-art techniques used to find approximate solutions of the brain sources giving rise to a scalp potential recording. Furthermore, a review of the performance results of the different techniques is provided to compare these different inverse solutions. The authors also include the results of a Monte-Carlo analysis which they performed to compare four non parametric algorithms and hence contribute to what is presently recorded in the literature. An extensive list of references to the work of other researchers is also provided.This paper starts off with a mathematical description of the inverse problem and proceeds to discuss the two main categories of methods which were developed to solve the EEG inverse problem, mainly the non parametric and parametric methods. The main difference between the two is to whether a fixed number of dipoles is assumed a priori or not. Various techniques falling within these categories are described including minimum norm estimates and their generalizations, LORETA, sLORETA, VARETA, S-MAP, ST-MAP, Backus-Gilbert, LAURA, Shrinking LORETA FOCUSS (SLF), SSLOFO and ALF for non parametric methods and beamforming techniques, BESA, subspace techniques such as MUSIC and methods derived from it, FINES, simulated annealing and computational intelligence algorithms for parametric methods. From a review of the performance of these techniques as documented in the literature, one could conclude that in most cases the LORETA solution gives satisfactory results. In situations involving clusters of dipoles, higher resolution algorithms such as MUSIC or FINES are however preferred. Imposing reliable biophysical and psychological constraints, as done by LAURA has given superior results. The Monte-Carlo analysis performed, comparing WMN, LORETA, sLORETA and SLF, for different noise levels and different simulated source depths has shown that for single source localization, regularized sLORETA gives the best solution in terms of both localization error and ghost sources. Furthermore the computationally intensive solution given by SLF was not found to give any additional benefits under such simulated conditions.

Review on solving the forward problem in EEG source analysis

BackgroundThe aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.MethodsWhile other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field.ResultsIt starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poissons differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poissons equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poissons equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method.ConclusionSolving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.

Functional Adaptive Control: An Intelligent Systems Approach

I. Introduction.- 1. Introduction.- 1.1 Intelligent Control Systems.- 1.2 Approaches to Intelligent Control.- 1.2.1 Contribution of Adaptive Control.- 1.2.2 Contribution of Artificial Intelligence.- 1.2.3 Confluence of Adaptive Control and AI: Intelligent Control.- 1.3 Enhancing the Performance of Intelligent Control.- 1.3.1 Multiple Model Schemes: Dealing with Complexity.- 1.3.2 Stochastic Adaptive Control: Dealing with Uncertainty.- 1.4 The Objectives and their Rationale.- II. Deterministic Systems.- 2. Adaptive Control of Nonlinear Systems.- 2.1 Introduction.- 2.2 Continuous-time Systems.- 2.2.1 Control by Feedback Linearization.- 2.2.2 Control by Backstepping.- 2.2.3 Adaptive Control.- 2.3 Discrete-time Systems.- 2.3.1 Affine Approximations and Feedback Linearization.- 2.3.2 Adaptive Control.- 2.4 Summary.- 3. Dynamic Strueture Networks for Stahle Adaptive Control.- 3.1 Introduction.- 3.2 Problem Formulation.- 3.3 Fixed-structure Network Solutions.- 3.4 Dynamic Network Structure.- 3.5 The Control Law and Error Dynamies.- 3.6 The Adaptive System.- 3.7 Stability Analysis.- 3.8 Evaluation of Control Parameters and Implementation.- 3.8.1 The Disturbanee Bound.- 3.8.2 Choice of the Boundary Layer.- 3.8.3 Comments.- 3.8.4 Implementation.- 3.9 Simulation Examples.- 3.9.1 Example 1.- 3.9.2 Example 2.- 3.10 Summary.- 4. Composite Adaptive Control of Continuous-Time Systems.- 4.1 Introduetion.- 4.2 Problem Formulation.- 4.3 The Neural Networks.- 4.4 The Control Law.- 4.5 Composite Adaptation.- 4.5.1 The Identifieation Model.- 4.5.2 The Adaptation Law.- 4.6 Stability Analysis.- 4.7 Determination of the Disturbanee Bounds.- 4.8 Simulation Examples.- 4.8.1 Example 1.- 4.8.2 Example 2.- 4.9 Summary.- 5. Funetional Adaptive Control of Discrete-Time Systems.- 5.1 Introduetion.- 5.2 Problem Formulation.- 5.3 The Neural Network.- 5.4 The Control Law.- 5.5 The Adaptive System.- 5.6 Stability Analysis.- 5.7 Traeking Error Convergenee.- 5.8 Simulation Examples.- 5.8.1 Example 1.- 5.8.2 Example 2.- 5.9 Extension to Adaptive Sliding Mode Control.- 5.9.1 Definitions of a Discrete-time Sliding Mode.- 5.9.2 Adaptive Sliding Mode Control.- 5.9.3 Problem Formulation.- 5.9.4 The Control Law.- 5.9.5 The Adaptive System.- 5.9.6 Stability Analysis.- 5.9.7 Sliding and Tracking Error Convergence.- 5.9.8 Simulation Example.- 5.10 Summary.- III. Stochastic Systems.- 6. Stochastic Control.- 6.1 Introduction.- 6.2 FUndamental Principles.- 6.3 Classes of Stochastic Control Problems.- 6.4 Dual Control.- 6.4.1 Degrees of Interaction.- 6.4.2 Solutions to the Implementation Problem.- 6.5 Conclusions.- 7. Dual Adaptive Control of Nonlinear Systems.- 7.1 Introduction.- 7.2 Problem Formulation.- 7.3 Dual Controller Design.- 7.3.1 GaRBF Dual Controller.- 7.3.2 Sigmoidal MLP Dual Controller.- 7.3.3 Analysis of the Control Laws.- 7.4 Simulation Examples and Performance Evaluation.- 7.4.1 Example 1.- 7.4.2 Example 2.- 7.5 Summary.- 8. Multiple Model Approaches.- 8.1 Introduction.- 8.2 Basic Formulation.- 8.2.1 Multiple Model Adaptive Contro!..- 8.2.2 Jump Systems.- 8.3 Adaptive IO Models.- 8.3.1 Scheduled Mode Transitions.- 8.4 Summary.- 9. Multiple Model Dual Adaptive Control of Jump Nonlinear Systems.- 9.1 Introduction.- 9.2 Problem Formulation.- 9.3 The Estimation Problem.- 9.3.1 Known Mode Case.- 9.3.2 Unknown Mode Case.- 9.4 Self-organized Allocation of Local Models.- 9.5 The Control Law.- 9.5.1 Known Mode Case.- 9.5.2 Unknown Mode Case.- 9.6 Simulation Examples and Performance Evaluation.- 9.6.1 Example 1.- 9.6.2 Example 2.- 9.7 Summary.- 10. Multiple Model Dual Adaptive Control of Spatial Multimodal Systems.- 10.1 Introduction.- 10.2 Problem Formulation.- 10.3 The Modular Network.- 10.4 The Estimation Problem.- 10.4.1 Local Model Parameter Estimation.- 10.4.2 Validity Function Estimation.- 10.5 The Control Law.- 10.5.1 Known System Case.- 10.5.2 Unknown System Case.- 10.6 Simulation Examples and Performance Evaluation.- 10.6.1 Example 1.- 10.6.2 Example 2.- 10.6.3 Performance Evaluation.- 10.7 Summary.- IV. Conclusions.- 11. Conclusions.- References.

Dual Adaptive Dynamic Control of Mobile Robots Using Neural Networks

This paper proposes two novel dual adaptive neural control schemes for the dynamic control of nonholonomic mobile robots. The two schemes are developed in discrete time, and the robots nonlinear dynamic functions are assumed to be unknown. Gaussian radial basis function and sigmoidal multilayer perceptron neural networks are used for function approximation. In each scheme, the unknown network parameters are estimated stochastically in real time, and no preliminary offline neural network training is used. In contrast to other adaptive techniques hitherto proposed in the literature on mobile robots, the dual control laws presented in this paper do not rely on the heuristic certainty equivalence property but account for the uncertainty in the estimates. This results in a major improvement in tracking performance, despite the plant uncertainty and unmodeled dynamics. Monte Carlo simulation and statistical hypothesis testing are used to illustrate the effectiveness of the two proposed stochastic controllers as applied to the trajectory-tracking problem of a differentially driven wheeled mobile robot.

Particle filtering-based fault detection in non-linear stochastic systems

Much of the development in model-based fault detection techniques for dynamic stochastic systems has relied on the system model being linear and the noise and disturbances being Gaussian. Linearized approximations have been used in the non-linear systems case. However, linearization techniques, being approximate, tend to suffer from poor detection or high false alarm rates. A novel particle filtering based approach to fault detection in non-linear stochastic systems is developed here. One of the appealing advantages of the new approach is that the complete probability distribution information of the state estimates from particle filter is utilized for fault detection, whereas, only the mean and covariance of an approximate Gaussian distribution are used in a coventional extended Kalman filter-based approach. Another advantage of the new approach is its applicability to general non-linear system with non-Gaussian noise and disturbances. The effectiveness of this new method is demonstrated through Monte Carlo simulations and the detection performance is compared with that using the extended Kalman filter on a non-linear system.

Brief paper: Dual adaptive control of nonlinear stochastic systems using neural networks

A suboptimal dual adaptive system is developed for control of stochastic, nonlinear, discrete time plants that are affine in the control input. The nonlinear functions are assumed to be unknown and neural networks are used to approximate them. Both Gaussian radial basis function and sigmoidal multilayer perceptron neural networks are considered and parameter adjustment is based on Kalman filtering. The result is a control law that takes into consideration the uncertainty of the parameter e stimates, thereby eliminating the need to perform prior open-loop plant identification. The performance of the system is analyzed by simulation and Monte Carlo analysis.

Order Estimation of Multivariate ARMA Models

Model order estimation is fundamental in the system identification process. In this paper, we generalize a previous multivariate autoregressive (AR) model order estimation method (J. Lardies and N. Larbi, ¿A new method for model order selection and model parameter estimation in time domain,¿ J. Sound Vibr., vol. 245, no. 2, 2001) to include multivariate autoregressive moving average (ARMA) models and propose a modified model order selection criterion. We discuss the performance analysis of the proposed criterion and show that it has a lower error probability for model order selection when compared to the criterion of G. Liang ¿ARMA model order estimation based on the eigenvalues of the covariance matrix,¿IEEE Trans. Signal Process., vol. 41, no. 10, pp. 3009-03009, Oct. 1993). A Monte-Carlo (MC) analysis of the model order selection performance under different noise variations and randomized model parameters is performed, allowing the MC results to be generalized across model parameter values and various noise levels. Finally we validate the model for both simulated data and real electroencephalographic (EEG) data by spectral fitting, using the model order selected by the proposed technique as compared to that selected by Akaikes Information Criterion (AIC). We demonstrate that with the proposed technique a better fit is obtained.

Scribbles to vectors: preparation of scribble drawings for CAD interpretation

This paper describes the work carried out on off-line paper based scribbles such that they can be incorporated into a sketch-based interface without forcing designers to change their natural drawing habits. In this work, the scribbled drawings are converted into a vectorial format which can be recognized by a CAD system. This is achieved by using pattern analysis techniques, namely the Gabor filter to simplify the scribbled drawing. Vector line are then extracted from the resulting drawing by means of Kalman filtering.

A sequential Monte Carlo filtering approach to fault detection and isolation in nonlinear systems

Much of the development in fault detection schemes have relied on the system being linear and the noise and disturbances being Gaussian. In such cases, optimal filtering ideas based on Kalman filtering is utilised in estimation followed by a residual analysis for which whiteness tests are typically carried out. Linearised approximations have been used in the nonlinear systems case. However, linearisation techniques, being approximate, tend to suffer from poor detection or high false alarm rates. In this paper, we use the sequential Monte Carlo filtering approach where the complete posterior distribution of the estimates are represented through samples or particles as opposed to the mean and covariance of an approximated Gaussian distribution. We compare the fault detection performance with that using the extended Kalman filtering and investigate the isolation performance on a nonlinear system.

Automatic detection of spindles and K-complexes in sleep EEG using switching multiple models

Abstract This work investigates the use of switching linear Gaussian state space models for the segmentation and automatic labelling of Stage 2 sleep EEG data characterised by spindles and K-complexes. The advantage of this approach is that it offers a unified framework of detecting multiple transient events within background EEG data. Specifically for the identification of background EEG, spindles and K-complexes, a true positive rate (false positive rate) of 76.04% (33.47%), 83.49% (47.26%) and 52.02% (7.73%) respectively was obtained on a sample by sample basis. A novel semi-supervised model allocation approach is also proposed, allowing new unknown modes to be learnt in real time.