Bayesian Algorithm Based Localization of EEG Recorded Electromagnetic Brain Activity

2019 ◽  
Vol 15 (2) ◽  
pp. 184-193
Author(s):  
Munsif Ali Jatoi ◽  
Nidal Kamel ◽  
Sayed Hyder Abbas Musavi ◽  
José David López
Keyword(s):  
Inverse Problem ◽  
Source Localization ◽  
Brain Activity ◽  
Research Work ◽  
Bayesian Framework ◽  
Forward Problem ◽  
Source Reconstruction ◽  
Eeg Data ◽  
Physical Task ◽  
Ill Posed

Background: Electrical signals are generated inside human brain due to any mental or physical task. This causes activation of several sources inside brain which are localized using various optimization algorithms. Methods: Such activity is recorded through various neuroimaging techniques like fMRI, EEG, MEG etc. EEG signals based localization is termed as EEG source localization. The source localization problem is defined by two complementary problems; the forward problem and the inverse problem. The forward problem involves the modeling how the electromagnetic sources cause measurement in sensor space, while the inverse problem refers to the estimation of the sources (causes) from observed data (consequences). Usually, this inverse problem is ill-posed. In other words, there are many solutions to the inverse problem that explains the same data. This ill-posed problem can be finessed by using prior information within a Bayesian framework. This research work discusses source reconstruction for EEG data using a Bayesian framework. In particular, MSP, LORETA and MNE are compared. Results: The results are compared in terms of variational free energy approximation to model evidence and in terms of variance accounted for in the sensor space. The results are taken for real time EEG data and synthetically generated EEG data at an SNR level of 10dB. Conclusion: In brief, it was seen that MSP has the highest evidence and lowest localization error when compared to classical models. Furthermore, the plausibility and consistency of the source reconstruction speaks to the ability of MSP technique to localize active brain sources.

scholarly journals ConvDip: A convolutional neural network for better M/EEG Source Imaging

2020 ◽  
Author(s):  
Lukas Hecker ◽  
Rebekka Rupprecht ◽  
Ludger Tebartz van Elst ◽  
Juergen Kornmeier
Keyword(s):  
Neural Network ◽  
Inverse Problem ◽  
Convolutional Neural Network ◽  
Brain Activity ◽  
Clinical Diagnostics ◽  
Dipole Model ◽  
Source Imaging ◽  
Eeg Source Imaging ◽  
Eeg Data ◽  
Inverse Solutions

AbstractEEG and MEG are well-established non-invasive methods in neuroscientific research and clinical diagnostics. Both methods provide a high temporal but low spatial resolution of brain activity. In order to gain insight about the spatial dynamics of the M/EEG one has to solve the inverse problem, which means that more than one configuration of neural sources can evoke one and the same distribution of EEG activity on the scalp. Artificial neural networks have been previously used successfully to find either one or two dipoles sources. These approaches, however, have never solved the inverse problem in a distributed dipole model with more than two dipole sources. We present ConvDip, a novel convolutional neural network (CNN) architecture that solves the EEG inverse problem in a distributed dipole model based on simulated EEG data. We show that (1) ConvDip learned to produce inverse solutions from a single time point of EEG data and (2) outperforms state-of-the-art methods (eLORETA and LCMV beamforming) on all focused performance measures. (3) It is more flexible when dealing with varying number of sources, produces less ghost sources and misses less real sources than the comparison methods. (4) It produces plausible inverse solutions for real-world EEG recordings and needs less than 40 ms for a single forward pass. Our results qualify ConvDip as an efficient and easy-to-apply novel method for source localization in EEG and MEG data, with high relevance for clinical applications, e.g. in epileptology and real time applications.

scholarly journals Comparison of EEG source localization using meromorphic approximation to fuzzy C-mean

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Leila Saeidias ◽  
Tahir Ahmad ◽  
Norma Alias ◽  
Mehdi Ghanbari
Keyword(s):  
Inverse Problem ◽  
Source Localization ◽  
Simulated Data ◽  
Point Sources ◽  
Approximation Techniques ◽  
Fuzzy C Means ◽  
Meromorphic Approximation ◽  
Comparison Results ◽  
Ill Posed ◽  
Eeg Source Localization

Electroencephalography (EEG) is a neuroimaging technique for localizing active sources within the brain, from knowledge of electromagneticmeasurements outside the head. Recognition of point sources from boundary measurements is an ill-posed inverse problem. InEEG, measurements areonly accessible at electrode positions, the number of sources is not known a prior. This paper proposes a comparison between two approaches for EEGsource localization. First method based on Meromorphic approximation techniques in the complex plane and second one belongs to EEG’s methodwhich is processed using Fuzzy C-Means (FCM). Comparison results on simulated data are used to verify the superior of the Meromorphicapproximation with regarding to Fuzzy c-means, due to it provides the way for solving inverse problem of EEG source localization in 3D from boundarymeasurement based on Harmon function in the innermost layer .

scholarly journals EEG Dipole Source Localization using Deep Neural Network

2022 ◽  
Vol 16 ◽  
pp. 132-140
Author(s):  
Zeng Hui ◽  
Li Ying ◽  
Wang Lingyue ◽  
Yin Ning ◽  
Yang Shuo
Keyword(s):  
Neural Network ◽  
Inverse Problem ◽  
Relative Error ◽  
Source Localization ◽  
Deep Neural Network ◽  
Absolute Error ◽  
Dipole Source ◽  
Head Model ◽  
Eeg Data ◽  
Eeg Inverse Problem

Electroencephalography (EEG) inverse problem is a typical inverse problem, in which the electrical activity within the brain is reconstructed based on EEG data collected from the scalp electrodes. In this paper, the four-layer concentric head model is used for simulation firstly, four deep neural network models including a multilayer perceptron (MLP) model and three convolutional neural networks (CNNs) are adopted to solve EEG inverse problem based on equal current dipole (ECD) model. In the simulations, 100,000 samples are generated randomly, of which 60% are used for network training and 20% are used for cross-validation. Eventually, the generalization performance of the model using the optimal function is measured by the errors in the rest 20% testing set. The experimental results show that the absolute error, relative error, mean positioning error and standard deviation of the four models are extremely low. The CNN with 6 convolutional layers and 3 pooling layers (CNN-3) is the best model. Its absolute error is about 0.015, its relative error is about 0.005, and its dipole position error is 0.040±0.029 cm. Furthermore, we use CNN-3 for source localization of the real EEG data in Working Memory. The results are in accord with physiological experience. The deep neural network method in our study needs fewer calculation parameters, takes less time, and has better positioning results.

Magnetoencephalography Source Estimation

2020 ◽  
pp. 81-94
Author(s):  
Matti S. Hämäläinen
Keyword(s):  
Inverse Problem ◽  
Neuronal Activity ◽  
Time Resolution ◽  
Brain Activity ◽  
Forward Modeling ◽  
Estimation Methods ◽  
Distributed Source ◽  
Source Estimation ◽  
Ill Posed ◽  
Anatomical Constraints

This chapter describes the source estimation approaches to magnetoencephalography (MEG) analysis. Both MEG and electroencephalography (EEG) are measures of ongoing neuronal activity, and are ultimately generated by the same sources: postsynaptic currents in groups of neurons which have a geometrical arrangement favoring currents with a uniform direction across nearby neurons. From the outset, the overarching theme of MEG analysis methods has been the desire to transform the signals measured by the MEG sensors outside the head into estimates of source activity. This problem is challenging because of the ill-posed nature of the electromagnetic inverse problem. However, thanks to being able to capitalize on appropriate physiological and anatomical constraints, several reliable and widely used source estimation methods have emerged. The chapter then identifies the forward modeling approaches needed to relate the signals in the source and sensor spaces, and characterizes two popular approaches to source estimation: the parametric dipole model and distributed source estimates. Until 50 years ago, electroencephalography (EEG) was the only noninvasive technique capable of directly measuring neuronal activity with a millisecond time resolution. However, with the birth of magnetoencephalography (MEG), functional brain activity can now be resolved with this time resolution at a new level of spatial detail. The use of MEG in practical studies began with the first real-time measurements in the beginning of 1970s. During the following decade, multichannel MEG systems were developed in parallel with both investigations of normal brain activity and clinical studies, especially in epileptic patients. The first whole-head MEG system with more than 100 channels was introduced in 1992. Up to now, such instruments have been delivered to researchers and clinicians worldwide. The overarching theme of MEG analysis methods has been from the outset the desire to transform the signals measured by the MEG sensors outside the head into estimates of source activity. This problem is challenging because of the ill-posed nature of the electromagnetic inverse problem. However, thanks to being able to capitalize on appropriate physiological and anatomical constraints, several reliable and widely used source estimation methods have emerged. This chapter starts by describing the overall characteristics of MEG, followed a general description of the source estimation problem. The chapter then discusses the forward modeling approaches needed to relate the signals in the source and sensor spaces, and finally characterizes two popular approaches to source estimation: the parametric dipole model and distributed source estimates.

scholarly journals A Regularization Process for Electrical Impedance Equation Employing Pseudoanalytic Function Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Cesar Marco Antonio Robles Gonzalez ◽  
Ariana Guadalupe Bucio Ramirez ◽  
Volodymyr Ponomaryov ◽  
Marco Pedro Ramirez Tachiquin
Keyword(s):  
Inverse Problem ◽  
Taylor Series ◽  
Regularization Method ◽  
Electrical Impedance ◽  
Function Theory ◽  
Forward Problem ◽  
Problem Method ◽  
Pseudoanalytic Function ◽  
Ill Posed

The electrical impedance equation is considered an ill-posed problem where the solution to the forward problem is more easy to achieve than the inverse problem. This work tries to improve convergence in the forward problem method, where the Pseudoanalytic Function Theory by means of the Taylor series in formal powers is used, incorporating a regularization method to make a solution more stable and to obtain better convergence. In addition, we include a comparison between the designed algorithms that perform proposed method with and without a regularization process and the autoadjustment parameter for this regularization process.

Statistical inversion in electrical impedance tomography using mixed total variation and non-convex ℓp regularization prior

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Thilo Strauss ◽  
Taufiquar Khan
Keyword(s):  
Inverse Problem ◽  
Total Variation ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Bayesian Framework ◽  
Electromagnetic Properties ◽  
Impedance Tomography ◽  
Conductivity Distribution ◽  
Ill Posed

AbstractElectrical impedance tomography (EIT) is a well-known technique to estimate the conductivity distribution γ of a body Ω with unknown electromagnetic properties. EIT is a severely ill-posed inverse problem. In this paper, we formulate the EIT problem in the Bayesian framework using mixed total variation (TV) and non-convex ℓ

scholarly journals Localizing Brain Activity from Multiple Distinct Sources via EEG

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
George Dassios ◽  
Michael Doschoris ◽  
Konstantia Satrazemi
Keyword(s):  
Inverse Problem ◽  
Surface Potential ◽  
Brain Activity ◽  
Sufficient Conditions ◽  
Measured Data ◽  
Single Dipole ◽  
Eeg Data ◽  
Necessary And Sufficient ◽  
Spherical Conductor ◽  
The Brain

An important question arousing in the framework of electroencephalography (EEG) is the possibility to recognize, by means of a recorded surface potential, the number of activated areas in the brain. In the present paper, employing a homogeneous spherical conductor serving as an approximation of the brain, we provide a criterion which determines whether the measured surface potential is evoked by a single or multiple localized neuronal excitations. We show that the uniqueness of the inverse problem for a single dipole is closely connected with attaining certain relations connecting the measured data. Further, we present the necessary and sufficient conditions which decide whether the collected data originates from a single dipole or from numerous dipoles. In the case where the EEG data arouses from multiple parallel dipoles, an isolation of the source is, in general, not possible.

scholarly journals Towards the Ensemble: IPCBR Model in Investigating Financial Bubbles

2020 ◽  
Vol 4 (4) ◽  
Author(s):  
Francis Ekpenyong ◽  
Georgios Samakovitis ◽  
Stelios Kapetanakis ◽  
Miltos Petridis
Keyword(s):  
Inverse Problem ◽  
Stock Market ◽  
Research Work ◽  
Problem Formulation ◽  
Forward Problem ◽  
Research Trend ◽  
Case Based Reasoning ◽  
Market Prices ◽  
Asset Bubbles ◽  
Pattern Description

Asset value predictability remains a major research concern in financial market especially when considering the effect of unprecedented market fluctuations on the behaviour of market participants. This paper presents preliminary results toward the building a reliable forward problem on ensemble approach IPCBR model, that leverages the capabilities of Case based Reasoning(CBR) and Inverse Problem Techniques (IPTs) to describe and model abnormal stock market fluctuations (often associated with asset bubbles) using datasets from historical stock market prices. The framework uses a rich set of past observations and geometric pattern description and then applies a CBR to formulate the forward problem, Inverse Problem formulation is then applied to identify a set of parameters that can statistically be associated with the occurrence of the observed patterns. This research work presents a formative strategy aimed to determine the causes of behaviour, rather than predict future time series points which brings a novel perspective to the problem of asset bubbles predictability, and a deviation from the existing research trend. The results depict the stock dynamics and statistical fluctuating evidence associated with the envisaged bubble problem.

Evaluation of Different EEG Source Localization Methods Using Testing Localization Errors

2013 ◽  
Vol 62 (3) ◽  
Author(s):  
Leila SaeidiAsl ◽  
Tahir Ahmad
Keyword(s):  
Inverse Problem ◽  
Source Localization ◽  
Forward Problem ◽  
Potential Fields ◽  
Uniqueness Property ◽  
Localization Errors ◽  
Source Models ◽  
Eeg Source Localization ◽  
The Brain ◽  
Dipolar Source

The ideas underlying the quantitative localization of the sources of the EEG review within the brain along with the current and emerging approaches to the problem. The ideas mentioned consist of distributed and dipolar source models and head models ranging from the spherical to the more realistic based on the boundary and finite elements. The forward and inverse problems in electroencephalography will debate. The inverse problem has non-uniqueness property in nature. More precisely, different combinations of sources can produce similar potential fields occur on the head. In contrast, the forward problem does have a unique solution. The forward problem calculates the potential field at the scalp from known source locations, source strengths and conductivity in the head, and it can be used to solve the inverse problem. In the final part of this paper, we compare the performance of three well–known EEG source localization techniques which applied to the underdetermined (distributed) source localization of the inverse problem. These techniques consist of LORETA, WMN and MN, which comparing by testing localization error.

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