An Adaptive Nonlinear Regularized Observer for Neural Activity Reconstruction

In this paper, a novel method for neural activity reconstruction based on an adaptive non-linear regularized observer is proposed. The regularized observer is based on a discrete nonlinear state space system that describe homogeneous activity into the brain by considering a physiologically meaningful model. In order to obtain an adequately performance of the nonlinear state equation, the parameters of the non-linear model are also estimated by using a multivariate non-linear least squares estimator resulting in an adaptive non-linear observer. Considering the complexity of the model and the large amount of states to be estimated, an iterative solution of the non-linear adaptive observer is proposed based on an IRA-L2 representation with spatial basis. A comparison of the performance of the algorithm in terms of relative error is analyzed, and also the evolution of the parameters is considered. A simulation framework based on the solution of a continuous non-linear differential equation that describe the neural activity in each source is used to evaluate against the multiple sparse priors method.