A Weighted Dynamic Inverse Problem for electroencephalographic current density reconstruction

A Weighted Dynamic Inverse Problem Solution is proposed for electroencephalographic current density reconstruction. The method considers physiologically based models that takes both spatial and temporal dynamics into account and a weighting stage to obtain the covariance of the measurement equation from observations. The calculated weighting matrix is included in the cost function used to solve the dynamic inverse problem. Additionally, an iterative method for inverse problem solution is proposed which considers the time varying weighting matrix in the solution. In this way, a weighted dynamic inverse problem solution is proposed including a time varying weighting matrix. The method performance is analyzed in terms of standard error, projected error, and residual error for several SNRs by using simulated signals through complex dynamical models.