LORETA‐contracting algorithm for solving EEG source distribution problems

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^TBW)⁻¹K^T{K(WB^TBW)⁻¹K^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.

Citation

Ma, X. and Guan, X. (2005), "LORETA‐contracting algorithm for solving EEG source distribution problems", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 24 No. 3, pp. 821-828. https://doi.org/10.1108/03321640510598166