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LORETA‐contracting algorithm for solving EEG source distribution problems

LORETA‐contracting algorithm for solving EEG source distribution problems Purpose – The electroencephalography (EEG) source tomography in bio‐electromagnetics is to estimate current dipole sources inside the brain from the measured electric potential distribution on the scalp surface. A traditional algorithm is the low‐resolution electromagnetic tomography algorithm (LORETA). In order to obtain high‐resolution tomography, the LORETA‐contracting algorithm is proposed. Design/methodology/approach – The relation between the dipolar current source J at the nodes in source region and the potential U at the observed points on the scalp surface can be expressed as a matrix equation U = KJ after discretization. K is a coefficient matrix. Usually its simultaneous equation is an under‐determined system. The LORETA approach is to find out min‖ BWJ ‖ 2 , under constraint U = KJ where B is the discrete Laplacian operator matrix, W is a weighting diagonal matrix. Its solution is J =( WB T BW ) −1 K T { K ( WB T BW ) −1 K T } + U where {} + denotes the Moore‐Penrose pseudo‐inverse matrix. The improvement on this approach is to establish an iterative program to repeat LORETA and reduce the number of unknown J quantities in the step i +1 by contracting the source region excluding some extreme little quantities of J given in the step i . The simultaneous equations will gradually turn to a properly determined system or to an over‐determined system. Finally, its solution can be obtained by using the least square method. Findings – Repeating to make the low‐resolution tomography by contracting the source region, we can get a high‐resolution tomography easily. Research limitations/implications – The LORETA‐contracting algorithm is based on the assumption that the dipolar current sources inside the brain are sparse and concentrated based on the physiological study of the brain activity. Originality/value – It is new to repeat LORETA combined with the contracting technique. This algorithm can be developed to solve EEG problems of realistic head models. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

LORETA‐contracting algorithm for solving EEG source distribution problems

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Publisher
Emerald Publishing
Copyright
Copyright © 2005 Emerald Group Publishing Limited. All rights reserved.
ISSN
0332-1649
DOI
10.1108/03321640510598166
Publisher site
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Abstract

Purpose – The electroencephalography (EEG) source tomography in bio‐electromagnetics is to estimate current dipole sources inside the brain from the measured electric potential distribution on the scalp surface. A traditional algorithm is the low‐resolution electromagnetic tomography algorithm (LORETA). In order to obtain high‐resolution tomography, the LORETA‐contracting algorithm is proposed. Design/methodology/approach – The relation between the dipolar current source J at the nodes in source region and the potential U at the observed points on the scalp surface can be expressed as a matrix equation U = KJ after discretization. K is a coefficient matrix. Usually its simultaneous equation is an under‐determined system. The LORETA approach is to find out min‖ BWJ ‖ 2 , under constraint U = KJ where B is the discrete Laplacian operator matrix, W is a weighting diagonal matrix. Its solution is J =( WB T BW ) −1 K T { K ( WB T BW ) −1 K T } + U where {} + denotes the Moore‐Penrose pseudo‐inverse matrix. The improvement on this approach is to establish an iterative program to repeat LORETA and reduce the number of unknown J quantities in the step i +1 by contracting the source region excluding some extreme little quantities of J given in the step i . The simultaneous equations will gradually turn to a properly determined system or to an over‐determined system. Finally, its solution can be obtained by using the least square method. Findings – Repeating to make the low‐resolution tomography by contracting the source region, we can get a high‐resolution tomography easily. Research limitations/implications – The LORETA‐contracting algorithm is based on the assumption that the dipolar current sources inside the brain are sparse and concentrated based on the physiological study of the brain activity. Originality/value – It is new to repeat LORETA combined with the contracting technique. This algorithm can be developed to solve EEG problems of realistic head models.

Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering – Emerald Publishing

Published: Sep 1, 2005

Keywords: Medical equipment; Electromagnetism; Radiography; Image processing

References

  • Computation of the potential distribution in a four layer an‐isotropic concentric spherical volume conductor
    Zhou, Hong; Oosterom, A.V.
  • Review of methods for solving the EEG inverse problem
    Pascual‐Marqui, R.D.
  • Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain
    Pascual‐Marqui, R.D.
  • Neuroelectric activity imaging based on a two‐stage weighted pseudo‐inverse algorithm
    Wu, Qing
  • Electric potential produced by a dipole in a homogeneous conducting sphere
    Yao, D.