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.

中文翻译：

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磁共振成像中头部运动的稀疏变化实时滤波

面对其他时间动态（例如功能激活），估计时变信号（例如根据磁共振成像数据的头部运动）变得特别具有挑战性。本文描述了一种新的类似卡尔曼滤波器的框架，该框架在测量模型中包含一个稀疏残差项。该附加项允许扩展卡尔曼滤波器在发生此类动态时生成适用于预期运动校正的实时运动估计。类似于乘法器的改变方向方法的迭代增广拉格朗日算法实现了此卡尔曼滤波器的更新步骤。本文从其对参数选择的敏感性方面评估了这种迭代方法对小运动和大运动的准确性和收敛速度。