Tikhonov regularization using a minimum-product criterion: Application to brain electrical tomography

Abstract

Tikhonov regularization is applied to the inversion of EEG potentials. The discrete model of the inversion problem results from an analytic technique providing information about extended intracranial distributions, with separate current source and sink positions. A three-layered concentric sphere model is used for representing head geometry. The selected regularization parameter is the minimizer of the product of the norm of the Tikhonov regularized solution and the norm of the corresponding residual. The simulations performed indicate that this regularization parameter selection method is more robust than the empirical composite residual and smoothing operator (CRESO) approach, in cases where only gaussian measurement noise exists in the discrete inverse model equation. Therefore the minimum product criterion can be used in real evoked potentials' data inversions, for the creation of brain electrical activity tomographic images, when the amount of noise present in the measured data is unknown.