AI 中文总结
该研究针对头颈部动态对比增强MRI的非线性运动抑制问题，基于柯普曼算子理论构建流程，测试了普通DMD、EDMD及神经网络版本，通过时间序列重复解决维度瓶颈，逐片处理图像分离运动与对比增强，实现有效运动抑制。
AI 中文摘要
我们基于柯普曼算子理论构建了一个运动抑制流程，该理论通过合适的数学‘透镜’（可观测量）将非线性动力学转化为线性动力学。我们测试了此想法的三个版本：直接作用于像素值的普通动态模态分解（DMD）、添加平方强度和空间梯度等物理特征以更好捕捉MRI信号与组织运动相互作用的扩展版本（EDMD）以及尝试自动学习最佳特征的神经网络版本。一个关键的实际贡献是时间序列重复：在分解前将整个时间序列平铺多次，这虽不改变潜在动力学，但为算法提供更多数据，解决了否则会阻止额外特征起作用的维度瓶颈问题。完整流程逐片工作，将每个图像分成小的重叠块，应用柯普曼提升和DMD基于特征频率分离慢速对比增强和快速运动，并将校正后的块重新融合在一起。
英文摘要
We build a motion suppression pipeline based on Koopman operator theory, which provides a way to turn nonlinear dynamics into linear ones by looking at the data through the right set of mathematical "lenses" (called observables). We test three versions of this idea: plain DMD that works directly on pixel values, an extended version (EDMD) that adds physically motivated features like squared intensities and spatial gradients to better capture how the MRI signal and tissue motion interact, and a neural network version that tries to learn the best features automatically. A key practical contribution is time-course repetition: we tile the entire temporal series multiple times before decomposition, which does not change the underlying dynamics but gives the algorithm more data to work with, fixing a dimensionality bottleneck that otherwise prevents the extra features from helping. The full pipeline works slice by slice, dividing each image into small overlapping blocks, applying the Koopman lifting and DMD to separate slow contrast enhancement from fast motion based on their characteristic frequencies, and blending the corrected blocks back together.
