Resumen de 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=(WBTBW)−1KT{K(WBTBW)−1KT}+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.
