Discrete, 3D distributed, linear imaging methods of electric neuronal activity. Part 1: exact, zero error localization

This paper deals with the EEG/MEG neuroimaging problem: given measurements of scalp electric potential differences (EEG: electroencephalogram) and extracranial magnetic fields (MEG: magnetoencephalogram), find the 3D distribution of the generating electric neuronal activity. This problem has no unique solution. Only particular solutions with "good" localization properties are of interest, since neuroimaging is concerned with the localization of brain function. In this paper, a general family of linear imaging methods with exact, zero error localization to point-test sources is presented. One particular member of this family is sLORETA (standardized low resolution brain electromagnetic tomography; Pascual-Marqui, Methods Find. Exp. Clin. Pharmacol. 2002, 24D:5-12; http://www.unizh.ch/keyinst/NewLORETA/sLORETA/sLORETA-Math01.pdf). It is shown here that sLORETA has no localization bias in the presence of measurement and biological noise. Another member of this family, denoted as eLORETA (exact low resolution brain electromagnetic tomography; Pascual-Marqui 2005: http://www.research-projects.unizh.ch/p6990.htm), is a genuine inverse solution (not merely a linear imaging method) with exact, zero error localization in the presence of measurement and structured biological noise. The general family of imaging methods is further extended to include data-dependent (adaptive) quasi-linear imaging methods, also with the exact, zero error localization property.