State Estimation of Hemodynamic Model for fMRI Under Confounds: SSM Method

Through hemodynamic models, the change of neuronal state can be estimated from functional magnetic resonance imaging (fMRI) signals. Usually, there are confounds in the fMRI signal, which will degrade the performance of the estimation for the neuronal state change. For the reason, this paper introduces a state-space model with confounds, from a conventional hemodynamic model. In this model, a successive state estimation method requires a state value vector, an error covariance, an innovation covariance, and a cross covariance to be re-derived. Thus, a confounds square-root cubature Kalman smoothing (CSCKS) algorithm is proposed in this paper. We use a Balloon-Windkessel model to generate simulation data and add confounds signals to evaluate the performance of the proposed algorithm. The experiment results show that when the signal-to-interference ratio is less than 21 dB, the CSCKS proposed in this paper reduced estimation error to 16%, whereas the traditional algorithm reduced it to only 73%.