Stochastic modeling of the PPG signal: a synthesis-by-analysis approach with applications

In this paper, we propose a stochastic model of photoplethysmographic signals that is able to synthesize an arbitrary number of other statistically equivalent signals to the one under analysis. To that end, we first preprocess the pulse signal to normalize and time-align pulses. In a second stage, we design a single-pulse model, which consists of ten parameters. In the third stage, the time evolution of this ten-parameter vector is approximated by means of two autoregressive moving average models, one for the trend and one for the residue; this model is applied after a decorrelation step which let us to process each vector component in parallel. The experiments carried out show that the model we here propose is able to maintain the main features of the original signal; this is accomplished by means of both a linear spectral analysis and also by comparing two measures obtained from a nonlinear analysis. Finally, we explore the capability of the model to: 1) track physical activity; 2) obtain statistics of clinical parameters by model sampling; and 3) recover corrupted or missing signal epochs by synthesis.