EEG source distribution localization using minimum-product and CRESO criteria for Tikhonov regularization

Electroencephalographic (EEG) inverse problems are often ill-posed due to the high condition number of the transfer matrix. In the present work simulated cortical source distributions are reconstructed, using a formulation providing information about extended intracranial distributions, with separate current source and sink positions. To overcome the influence of noise on measured voltages, as expected in real laboratory recordings, the Tikhonov regularization technique (TRT) is used for solving the discrete inverse problem matrix equation. Two criteria are used and compared in providing an approximation to the optimal regularization parameter, the composite residual and smoothing operator (CRESO) criterion and the minimum-product (MP) criterion. For levels of Gaussian measurement noise equal to or greater than 10%, the CRESO criterion performed significantly better than MP criterion, provided that the application of both criteria was extended to include as approximations even boundary regularization parameter values.