De-shape short time Fourier transform, wave-shape manifold, and medical applications
An innovative and adaptive acquisition of correct features from massive datasets with solid mathematical support is the core of modern data analysis. One particular interest in the medical field is extracting the hidden dynamics from the observed non-stationary time series, which is composed of multiple oscillatory signals with non-sinusoidal oscillations, time varying amplitude, and time varying frequency, while contaminated by a heteroscedastic noise. In this talk, I will show a novel combination of a new nonlinear time frequency analysis, called the de-shape short time Fourier transform, and the wave-shape manifold algorithm to solve this problem. We then apply the developed method to at least two medical problems -- (1) extract fetal ECG signal from the single lead maternal abdominal ECG signal; (2) extract instantaneous heart rate and instantaneous respiratory rate from the PPG signal during exercise. Their theoretical properties will be discussed or referred to https://arxiv.org/abs/1605.01805 (published in JFAA).