Inverse electroencephalography for volumetric sources

In this work the problem of recovering bioelectrical sources on the cerebral volume, from measurement of the potential generated by these sources on the scalp, is studied. This problem is an ill posed problem, since given a measurement on the scalp, there are different bioelectrical sources that produce this measurement and small variations in the input data can produce significant variations in the source localization. The problem is studied through a boundary value problem, which is obtained using a model that describes the head as a conductive layer medium. This model allows relationships between the characteristics of the bioelectrical activity and the EEG to be established. We find in this work conditions under which the inverse solution is unique and we give an algorithm to find it. In the simple case, when the head is modeled through two concentric circles, we give a regularization strategy.