How Mathematics can help in sensing instantaneous physiological information from photoplethysmography in a fast and reliable way

Despite the population of the noninvasive, economic, comfortable, and easy-to-install photoplethysmography (PPG) sensor, a mathematically rigorous and stable algorithm to simultaneously extract the fundamental physiological information, including the instantaneous heart rate (IHR) and the instantaneous respiratory rate (IRR), from the single-channel PPG signal is lacking. A novel signal processing technique, called the de-shape synchrosqueezing transform, is provided to tackle this challenging task. The algorithm is applied to two publicly available batch databases, one is collected during intense physical activities, for the reproducibility purpose and the state-of-the-art results are obtained compared with existing reported outcomes. The results suggest the potential of the proposed algorithm to analyze the signal acquired from the widely available wearable devices, even when a subject exercises. keyword: de-shape synchrosqueezing transform, photoplethysmography, instantaneous heart rate, instantaneous respiratory rate