Detrend-free hemodynamic data assimilation of two-stage Kalman estimator.

Spurious temporal drift is abundant in fMRI data, and its removal is a critical preprocessing step in fMRI data assimilation due to the sparse nature and the complexity of the data. Conventional data-driven approaches rest upon specific assumptions of the drift structure and signal statistics, and may lead to inaccurate results. In this paper we present an approach to the assimilation of nonlinear hemodynamic system, with special attention on drift. By treating the drift variation as a random-walk process, the assimilation problem was translated into the identification of a nonlinear system in the presence of time varying bias. We developed two-stage unscented Kalman filter (UKF) to efficiently handle this problem. In this framework the assimilation can implement with original fMRI data without detrending preprocessing. The fMRI responses and drift were estimated simultaneously in an assimilation cycle. The efficacy of this approach is demonstrated in synthetic and real fMRI experiments. Results show that the joint estimation strategy produces more accurate estimation of physiological states, fMRI response and drift than separate processing due to no assumption of structure of the drift that is not available in fMRI data.