Estimation of intra-cranial neural activities by means of regularized neural-network-based inversion techniques

Artificial neural networks can be exploited to solve inverse problems arising from the estimation of neural activities in the brain. In this paper, we review the network inversion techniques for solving inverse problems with special attention directed towards electroencephalographic dipole localization and the improvement of positron emission tomography. In our regularized network inversion technique, for stabilizing the solution, we explicitly include the a priori knowledge by adding penalty terms to the energy function and/or build this knowledge into the architecture of the multi-layered neural networks that are used as an inverse problem solver. In the electroencephalogram analysis, the consensus term added to the energy function facilitated 3-dipole localization for visually evoked potentials. Effectiveness of our regularization is shown in improving the positron emission tomographic images and for generating metabolic images of the brain, under the constraints given by the a priori knowledge inherent to the measurement systems and physiological rules.