SPARE: A Spectral Peak Recovery Algorithm for PPG Signals Pulsewave Reconstruction in Multimodal Wearable Devices

Figures

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  Figure 1. Photoplethysmographic (PPG) signals and corresponding spectra. (a,c) represent a PPG signal of a subject at rest and performing physical exercises with MA, respectively. (b,d) show the corresponding single-sided amplitude spectrum. The spectral peak that corresponds to the cardiac rhythm is marked with a red dot.

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  Figure 2. Example of a PPG signal reconstruction (and the spectrum of the reconstructed signal) keeping nothing but its fundamental frequency, second harmonic, and third one.

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  Figure 3. Block diagram of the SPARE algorithm. SSA: singular spectrum analysis, SSR: sparse signal reconstruction, FFT: fast Fourier transform, HR: heart rate, RR interval: beat-to-beat time interval detected from the electrocardiogram (ECG).

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  Figure 4. Decomposition of a PPG signal by means of singular spectrum analysis into five additive subcomponents.

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  Figure 5. Example of harmonic relation estimation. In green, the candidate peaks for the fundamental, second harmonic, and third harmonic. In red, the detected fundamental, second harmonic, and third one. Fundcand: set of peaks whose frequency is less than 10 BPM away from meanHR, Secondcand: set of p peaks whose frequency is closer to two times meanHR, Thirdcand: set of p peaks whose frequency is closer to three times meanHR. In this example, p has a value of 3.

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  Figure 6. Example of noisy PPG signal and its spectrum. Both original and reconstructed are reported.

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  Figure 7. Biomarkers and fiducial points extracted from ECG and PPG signals. PRT: pulse rising time, PDT: pulse decreasing time, PA: pulse amplitude, PP: pulse period, PW: pulse width, RR interval: beat-to-beat time interval detected from the ECG.

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  Figure 8. (Top) Reference PPG and PPG corrupted by noise using the synthetic noise generator at three different intensity levels (σ = 100, 200, and 500, T=500, and stride=100). (Bottom) PPG signal naturally corrupted by noise during physical activity.

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  Figure 9. Average and standard deviation of geometric mean between sensitivity and specificity for the detection of slope, peak, onset, and dicrotic points at different noise levels with SPARE (blue line), fastSPARE (yellow line), and raw data (orange line). All experiments were run for five random seeds each (for noise generation).

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  Figure 10. Mean square error (MSE) between the original PPG signal and the reconstructed one by SPARE and fastSPARE at different noise levels. For comparison, the MSE between the PPG signal without SPARE and the reference is also reported (orange line).