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 An inverse problem for the non-self-adjoint matrix Sturm-Liouville operator

2018 ◽  
Vol 50 (1) ◽  
pp. 71-102 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problem ◽  
Liouville Operator ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Sufficient Conditions ◽  
Adjoint Matrix ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Necessary And Sufficient

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary and sufficient conditions for the solvability of the inverse problem. Our approach is based on the constructive solution of the inverse problem by the method of spectral mappings. The characterization of the spectral data in the self-adjoint case is given as a corollary of the main result.

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 The Localization of Activity Sources in a Three-Dimensional Model of the Human Brain Using the Joint Analysis of EEG / sMRI Data

2019 ◽  
Vol 17 (3) ◽  
pp. 18-28
Author(s):  
E. Bykova ◽  
A. Savostyanov
Keyword(s):  
Inverse Problem ◽  
Brain Activity ◽  
Three Dimensional ◽  
Human Head ◽  
Joint Analysis ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Use Of Data ◽  
The Individual ◽  
The Brain

Despite the large number of existing methods of the diagnosis of the brain, brain remains the least studied part of the human body. Electroencephalography (EEG) is one of the most popular methods of studying of brain activity due to its relative cheapness, harmless, and mobility of equipment. While analyzing the EEG data of the brain, the problem of solving of the inverse problem of electroencephalography, the localization of the sources of electrical activity of the brain, arises. This problem can be formulated as follows: according to the signals recorded on the surface of the head, it is necessary to determine the location of sources of these signals in the brain. The purpose of my research is to develop a software system for localization of brain activity sources based on the joint analysis of EEG and sMRI data. There are various approaches to solving of the inverse problem of EEG. To obtain the most exact results, some of them involve the use of data on the individual anatomy of the human head – structural magnetic resonance imaging (sMRI data). In this paper, one of these approaches is supposed to be used – Electromagnetic Spatiotemporal Independent Component Analysis (EMSICA) proposed by A. Tsai. The article describes the main stages of the system, such as preprocessing of the initial data; the calculation of the special matrix of the EMSICA approach, the values of which show the level of activity of a certain part of the brain; visualization of brain activity sources on its three-dimensional model.

scholarly journals Estimation of the Directions of Alpha Rhythm Elementary Sources Using the Method of Human Brain Functional Tomography Based On the Magnetic Encephalography Data

2018 ◽  
Vol 13 (2) ◽  
pp. 426-436 ◽  
Author(s):  
M.N. Ustinin ◽  
S.D. Rykunov ◽  
A.I. Boyko ◽  
O.A. Maslova ◽  
K.D. Walton ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Time Series ◽  
Human Brain ◽  
Alpha Rhythm ◽  
Brain Activity ◽  
Problem Solution ◽  
New York University ◽  
Magnetic Encephalography ◽  
The Brain ◽  
Calculation Grid

New method for the magnetic encephalography data analysis was proposed. The method transforms multichannel time series into the spatial structure of the human brain activity. In this paper we further develop this method to determine the dominant direction of the electrical sources of brain activity at each node of the calculation grid. We have considered the experimental data, obtained with three 275-channel magnetic encephalographs in New York University, McGill University and Montreal University. The human alpha rhythm phenomenon was selected as a model object. Magnetic encephalograms of the brain spontaneous activity were registered for 5-7 minutes in magnetically shielded room. Detailed multichannel spectra were obtained by the Fourier transform of the whole time series. For all spectral components, the inverse problem was solved in elementary current dipole model and the functional structure of the brain activity was calculated in the frequency band 8-12 Hz. In order to estimate the local activity direction, at the each node of calculation grid the vector of the inverse problem solution was selected, having the maximal spectral power. So, the 3D-map of the brain activity vector field was produced – the directional functional tomogram. Such maps were generated for 15 subjects and some common patterns were revealed in the directions of the alpha rhythm elementary sources. The proposed method can be used to study the local properties of the brain activity in any spectral band and in any brain compartment.

Classification Algorithms for EEG-Based Brain-Computer Interface

2019 ◽  
pp. 52-73
Author(s):  
Sravanth Kumar Ramakuri ◽  
Chinmay Chakraboirty ◽  
Anudeep Peddi ◽  
Bharat Gupta
Keyword(s):  
Brain Activity ◽  
Biomedical Signal Processing ◽  
Computer Interface ◽  
Eeg Signals ◽  
Large Sets ◽  
Eeg Data ◽  
Important Measurement ◽  
The Brain

In recent years, a vast research is concentrated towards the development of electroencephalography (EEG)-based human-computer interface in order to enhance the quality of life for medical as well as nonmedical applications. The EEG is an important measurement of brain activity and has great potential in helping in the diagnosis and treatment of mental and brain neuro-degenerative diseases and abnormalities. In this chapter, the authors discuss the classification of EEG signals as a key issue in biomedical research for identification and evaluation of the brain activity. Identification of various types of EEG signals is a complicated problem, requiring the analysis of large sets of EEG data. Representative features from a large dataset play an important role in classifying EEG signals in the field of biomedical signal processing. So, to reduce the above problem, this research uses three methods to classify through feature extraction and classification schemes.

Reconstruction of a convolution operator from the right-hand side on the semiaxis

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Anatoly F. Voronin
Keyword(s):  
Inverse Problem ◽  
Integral Operator ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Explicit Formulas ◽  
Right Hand ◽  
The Right ◽  
Necessary And Sufficient ◽  
Operator Kernel ◽  
Problem Solvability

AbstractIn this paper, a Volterra integral equation of the first kind in convolutions on the semiaxis when the integral operator kernel and the right-hand side of the equation have a bounded support is considered. An inverse problem of reconstructing the solution to the equation and the integral operator kernel from values of the right-hand side is formulated. Necessary and sufficient conditions for the inverse problem solvability are obtained. A uniqueness and stability theorem is proved. Explicit formulas for reconstruction of the solution and kernel are obtained.

On Solutions of Inverse Problem for Hermitian Generalized Hamiltonian Matrices

2013 ◽  
Vol 860-863 ◽  
pp. 2727-2731
Author(s):  
Kai Fu Liang ◽  
Ming Jun Li ◽  
Ze Lin Zhu
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Design Automation ◽  
Sufficient Conditions ◽  
Matrix Equations ◽  
Complex Matrix ◽  
Linear Quadratic ◽  
Real Representation ◽  
The Matrix ◽  
Necessary And Sufficient

Hamiltonian matrices have many applications to design automation and autocontrol, in particular in the linear-quadratic autocontrol problem. This paper studies the inverse problems of generalized Hamiltonian matrices for matrix equations. By real representation of complex matrix, we give the necessary and sufficient conditions for the existence of a Hermitian generalized Hamiltonian solutions to the matrix equations, and then derive the representation of the general solutions.

Inverse problem about two-spectra for finite Jacobi matrices with zero diagonal

2016 ◽  
Vol 24 (6) ◽  
Author(s):  
Adil Huseynov
Keyword(s):  
Inverse Problem ◽  
Finite Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Jacobi Matrices ◽  
The Matrix ◽  
Explicit Procedure ◽  
Necessary And Sufficient

AbstractThe necessary and sufficient conditions for solvability of the inverse problem about two-spectra for finite order real Jacobi matrices with zero-diagonal elements are established. An explicit procedure of reconstruction of the matrix from the two-spectra is given.

Metrizability problem for spray on Lie algebroids

2016 ◽  
Vol 13 (09) ◽  
pp. 1650115
Author(s):  
Zahra Pirbodaghi ◽  
Morteza Mir Mohammad Rezaii
Keyword(s):  
Inverse Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Lie Algebroids ◽  
Jacobi Endomorphism ◽  
Necessary And Sufficient

In this paper, we study inverse problem for sprays on Lie algebroids. We obtain necessary and sufficient conditions, based on semi-basic forms, for a spray to be Lagrangian. Then we discuss the Finsler metrizability of a spray and obtain some equations on the Jacobi endomorphism.

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