How nonlinear-type time-frequency analysis can help in sensing instantaneous heart rate and instantaneous respiratory rate from photoplethysmography in a reliable way

Despite the population of the noninvasive, economic, comfortable, and easy-to-install photoplethysmography (PPG), it is still lacking a mathematically rigorous and stable algorithm which is able to simultaneously extract from a single-channel PPG signal the instantaneous heart rate (IHR) and the instantaneous respiratory rate (IRR). In this paper, a novel algorithm called deppG is provided to tackle this challenge. deppG is composed of two theoretically solid nonlinear-type time-frequency analyses techniques, the de-shape short time Fourier transform and the synchrosqueezing transform, which allows us to extract the instantaneous physiological information from the PPG signal in a reliable way. To test its performance, in addition to validating the algorithm by a simulated signal and discussing the meaning of "instantaneous", the algorithm is applied to two publicly available batch databases, the Capnobase and the ICASSP 2015 signal processing cup. The former contains PPG signals relative to spontaneous or controlled breathing in static patients, and the latter is made up of PPG signals collected from subjects doing intense physical activities. The accuracies of the estimated IHR and IRR are compared with the ones obtained by other methods, and represent the state-of-the-art in this field of research. The results suggest the potential of deppG to extract instantaneous physiological information from a signal acquired from widely available wearable devices, even when a subject carries out intense physical activities.