发表机构
Georgia Tech; Emory University（佐治亚理工学院; 埃默里大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出圆柱测地流匹配方法，以几何正确的相位-振幅路径替代仿射插值，用于准周期生理信号配对变换，在零样本PPG和SCG基准上显著降低距离误差。
AI 中文摘要
准周期生理波形之间的配对变换（即从源信号恢复目标振荡信号）对于解读来自身体不同部位可穿戴设备的心血管信号至关重要。这些问题中的源到目标映射具有固有的几何结构：相位围绕周期缠绕，必须作为圆形变量处理；振幅保持严格为正；且逐拍对齐可能在不同周期和受试者之间不可预测地漂移。尽管深度神经网络已被用于相位估计和复值信号建模，但先前的工作并未显式学习配对信号之间的相位传输。因此，端点监督回归和流匹配中使用的标准仿射路径均未考虑这种相位-振幅结构。我们引入了用于配对心血管波形变换的圆柱测地流匹配。我们表明，流匹配中使用的标准仿射路径在准周期信号之间插值时会使中间振幅和瞬时频率失真；将其替换为相位-振幅圆柱上的闭式测地线可消除这些伪影，并将每个训练对转换为密集的、几何一致的速度监督。在零样本光电容积脉搏波和有限支持的心震图自适应基准上，我们的方法始终优于插值基线，并达到或超过直接监督预测，在最强竞争基线上将希尔伯特变换、$L_2$和动态时间规整距离最多减少约$15\%$。这些结果表明，桥接几何是振荡信号变换流匹配的关键归纳偏置。
英文摘要
Paired translation between quasiperiodic physiological waveforms (i.e., recovering a target oscillatory signal from the source) is central to the interpretation of cardiovascular signals derived from wearables placed at different body locations. This source-to-target mapping in these problems carries inherent geometric structure: the phase wraps around the cycle and must be treated as a circular variable, the amplitude remains strictly positive, and the beat-to-beat alignment can drift unpredictably across cycles and subjects. While deep neural networks have been used for phase estimation and complex-valued signal modeling, prior work does not explicitly learn phase transport between paired signals. Consequently, neither endpoint-supervised regression nor the standard affine path used in flow matching accounts for this phase--amplitude structure. We introduce \emph{cylindrical geodesic flow matching} for paired cardiovascular waveform translation. We show that the standard affine path used in flow matching distorts intermediate amplitude and instantaneous frequency when interpolating between quasiperiodic signals; replacing it with a closed-form geodesic on the phase--amplitude cylinder eliminates these artifacts and converts each training pair into dense, geometry-consistent velocity supervision. On zero-shot photoplethysmography and limited-support seismocardiography adaptation benchmarks, our method consistently outperforms interpolation baselines and matches or exceeds direct supervised prediction, reducing Hilbert Transform, $L_2$, and Dynamic Time Warping distance by up to ${\sim}15\%$ over the strongest competing baseline. These results suggest that bridge geometry is a critical inductive bias for flow matching on oscillatory signal translation.
