Unveiling Nonstationary Biorhythms: Landmark Diffusion and Its Clinical Applications

Hau-Tieng Wu, New York University
Fine Hall 214

Compared with the commonly collected health information, the wealth of information offered by long-term, high-frequency physiological time series with nonstationary characteristics is hindered by challenges in extracting clinically relevant insights. To address these obstacles, we present a novel signal processing approach rooted in latent diffusion geometry. Our method is purpose-built to effortlessly handle vast datasets, including ultra-long, high-frequency time series, while maintaining robustness against color and heterogeneous noise, supported by rigorous theory. Additionally, we demonstrate its ability to accurately reconstruct the spectral structure of the Laplace-Beltrami operator, achieving L-infinity convergence. We illustrate the practical utility of this technique in evaluating clinical outcomes of liver transplants by unveiling subtle features concealed within arterial blood pressure signals, imperceptible to the naked eye.