Wyatt C L, Ari N, Kraft R A
Virginia Tech, USA.
Inf Process Med Imaging. 2005;19:738-49. doi: 10.1007/11505730_61.
Spherical navigators are an attractive approach to motion compensation in Magnetic Resonance Imaging. Because they can be acquired quickly, spherical navigators have the potential to measure and correct for rigid motion during image acquisition (prospectively as opposed to retrospectively). A limiting factor to prospective use of navigators is the time required to estimate the motion parameters. This estimation problem can be separated into a rotational and translational component. Recovery of the rotational motion can be cast as a registration of functions defined on a sphere. Previous methods for solving this registration problem are based on optimization strategies that are iterative and require k-space interpolation. Such approaches have undesirable convergence behavior for prospective use since the estimation complexity depends on both the number of samples and the amount of rotation. We propose and demonstrate an efficient algorithm for recovery of rotational motion using spherical navigators. We decompose the navigator magnitude using the spherical harmonic transform. In this framework, rigid rotations can be recovered from an over-constrained system of equations, leading to a computationally efficient algorithm for prospective motion compensation. The resulting algorithm is compared to existing approaches in simulated and actual navigator data. These results show that the spherical harmonic based estimation algorithm is significantly faster than existing methods and so is suited for prospective motion correction.
球形导航器是磁共振成像中运动补偿的一种有吸引力的方法。由于球形导航器可以快速采集，因此有潜力在图像采集期间（前瞻性而非回顾性）测量并校正刚体运动。导航器前瞻性应用的一个限制因素是估计运动参数所需的时间。这个估计问题可以分为旋转和平移分量。旋转运动的恢复可以转化为球面上定义的函数的配准。以前解决这个配准问题的方法基于迭代且需要k空间插值的优化策略。由于估计复杂度取决于样本数量和旋转量，这些方法在前瞻性应用中具有不良的收敛行为。我们提出并演示了一种使用球形导航器恢复旋转运动的高效算法。我们使用球谐变换分解导航器幅度。在此框架下，刚体旋转可以从一个超定方程组中恢复，从而得到一种用于前瞻性运动补偿的计算高效的算法。将所得算法与模拟和实际导航器数据中的现有方法进行比较。这些结果表明，基于球谐的估计算法比现有方法快得多，因此适用于前瞻性运动校正。
