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 parallel to BWJ parallel to(2), under constraint U = KJ where B is the discrete Laplacian operator matrix, W is a weighting diagonal matrix. Its solution is J = ((WBBW)-B-T)K--1(T) {K((WBBW)-B-T)K-1 (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.
electromagnetism medical equipment radiography image processing