Hard Inverse problem: HIP

Zero Dipole Localization Error Rolando Grave de Peralta,1,2 Olaf Hauk,3 and Sara L. Gonzalez1 1Electrical Neuroimaging Group, Neurology Department, Geneva University Hospital, 24 Rue Micheli du Crest, 1211 Geneva 14, Switzerland 2Neurodynamics Laboratory, Department of Psychiatry and Clinical Psychobiology, University of Barcelona, 08035 Barcelona, Catalonia, Spain 3Cognition and Brain Sciences Unit, Medical Research Council, 15 Chaucer Road, Cambridge, CB2 7EF, UK A tomography of neural sources could be constructed from EEG/MEG recordings once the neuroelectromagnetic inverse problem (NIP) is solved. Unfortunately the NIP lacks a unique solution and therefore additional constraints are needed to achieve uniqueness. Researchers are then confronted with the dilemma of choosing one solution on the basis of the advantages publicized by their authors. This study aims to help researchers to better guide their choices by clarifying what is hidden behind inverse solutions oversold by their apparently optimal properties to localize single sources. Here, we introduce an inverse solution (ANA) attaining perfect localization of single sources to illustrate how spurious sources emerge and destroy the reconstruction of simultaneously active sources. Although ANA is probably the simplest and robust alternative for data generated by a single dominant source plus noise, the main contribution of this manuscript is to show that zero localization error of single sources is a trivial and largely uninformative property unable to predict the performance of an inverse solution in presence of simultaneously active sources. We recommend as the most logical strategy for solving the NIP the incorporation of sound additional a priori information about neural generators that supplements the information contained in the data.