Concurrent bias correction in hemodynamic data assimilation

Low-frequency drift in fMRI datasets can be caused by various sources and are generally not of interest in a conventional task-based fMRI experiment. This feature complicates the assimilation approach that is always under specific assumption on statistics of system uncertainties. In this paper, we present a novel approach to the assimilation of nonlinear hemodynamic system with stochastic biased noise. 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 a bias aware unscented Kalman estimator to efficiently handle this problem. In this framework, the estimates of bias-free states and drift are separately carried out in two parallel filters, the optimal estimates of the system states then are corrected from bias-free states with drift estimates. The approach can simultaneously deal with the fMRI responses and drift in an assimilation cycle in an on-line fashion. It makes no assumptions of the structure and statistics of the drift, thereby is particularly suited for fMRI imaging where the formulation of real drift remains difficult to acquire. Experiments with synthetic data and real fMRI data are performed to demonstrate feasibility of our approach and to explore its potential advantages over classic polynomial approach. Moreover, we include the comparison of the variability of observables from the scanner and of normalized signal used in assimilation procedure in Appendix.