A Synchronous Detection Algorithm for Quasi-Periodic Signal Components and Its Application in Photoplethysmographic Imaging

photoplethysmographic imaging (PPI) is a noninvasive method for assessing local blood flow beneath the skin surface by a video camera. The synchronization detection algorithm based on lock-in amplification (LIA) is a widely used method to obtain PPI. This method can obtain two maps: one is the amplitude map, which represents the strength of the PPG signal, and the other is the pulse-transit-time (PTT) map, which represents the time synchronization of the PPG signal. The latter is usually represented directly in form of a phase map. However, in general, the frequency of PPG signals is time-varying and contains harmonic components, which complicates the application of the algorithm. This article analyzes the relationship between the LIA calculation results and the time delay when the frequency of the signal is time-varying or the signal contains harmonics. Theoretical analysis results show that, when the signal contains harmonic components, the relationship between time delay and phase is approximately linear only when the time delay is not very large or the harmonic components are not very strong. Meanwhile, amplitude appears as a “bell-shaped” function, with its peak value located at the zero time delay. Video data were acquired by the video PPG acquisition system built in our laboratory, and the PPI was calculated by the synchronous detection algorithm using a reference signal generated directly by the Hilbert transform of an actual signal. Experiments show that the proposed method can obtain more stable results than using a constant-frequency reference signal when dealing with time-varying heart rate data. An interesting finding is that, when the reference signal contains harmonic components, PPG distribution features in the amplitude map can be enhanced.