The inverse electroencephalographic problem (IEP) consists in finding the bioelectrical sources concentrated in the cerebral volume from measurements of the potential generated by these sources on the scalp (EEG). The IEP 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 localization of the source. This problem has been studied through a boundary value problem, which is obtained using a model that describes the head as a conductive medium which is divided into two disjoint regions: the former represents the brain and the latter the rest of the head. Results presented in this work, can be extended to more conductive layers. In this model, each region has a constant conductivity and the cavities that correspond to eyes, nose and neck are neglected. Conditions under which the IEP has a unique solution (there is a unique harmonic function, defined in the region that represents the brain, that produces the EEG) have been given using this model. In this work, we give, when the head is modeled using two concentric spheres, a regularization strategy in order to obtain a stable algorithm for the IEP.

EEG, inverse problem, Cauchy problem, regularization strategy, harmonics spherical.