Real-Time Filtering with Sparse Variations for Head Motion in Magnetic Resonance Imaging

Estimating a time-varying signal, such as head motion from magnetic resonance imaging data, becomes particularly challenging in the face of other temporal dynamics such as functional activation. This paper describes a new Kalman filter-like framework that includes a sparse residual term in the measurement model. This additional term allows the extended Kalman filter to generate real-time motion estimates suitable for prospective motion correction when such dynamics occur. An iterative augmented Lagrangian algorithm similar to the alterating direction method of multipliers implements the update step for this Kalman filter. This paper evaluates the accuracy and convergence rate of this iterative method for small and large motion in terms of its sensitivity to parameter selection. The included experiment on a simulated functional magnetic resonance imaging acquisition demonstrates that the resulting method improves the maximum Youden's J index of the time series analysis by 2-3% versus retrospective motion correction, while the sensitivity index increases from 4.3 to 5.4 when combining prospective and retrospective correction.