In computed tomography (CT), the projection geometry used for data acquisition needs to be known precisely to obtain a clear reconstructed image. Rigid patient motion is a cause for misalignment between measured data and employed geometry. Commonly, such motion is compensated by solving an optimization problem that, e.g., maximizes the quality of the reconstructed image with respect to the projection geometry. So far, gradient-free optimization algorithms have been utilized to find the solution for this problem. Here, we show that gradient-based optimization algorithms are a possible alternative and compare the performance to their gradient-free counterparts on a benchmark motion compensation problem. Gradient-based algorithms converge substantially faster while being comparable to gradient-free algorithms in terms of capture range and robustness to the number of free parameters. Hence, gradient-based optimization is a viable alternative for the given type of problems.

翻译：在计算机断层扫描（CT）中，用于数据采集的投影几何结构需要精确已知，才能获得清晰的图像重建结果。患者刚体运动是导致测量数据与所使用几何结构之间失配的原因之一。通常，通过求解一个优化问题来补偿此类运动，例如，该问题通过最大化重建图像相对于投影几何结构的质量来实现。目前，已有研究利用无梯度优化算法解决该问题。本文证明，基于梯度的优化算法是一种可行的替代方案，并在基准运动补偿问题上对比了其与无梯度算法的性能。基于梯度的算法收敛速度显著更快，同时在捕获范围和自由参数数量鲁棒性方面与无梯度算法相当。因此，对于所述问题类型，基于梯度的优化是一种可行的替代方法。