Signal processing
Compressed Sensing for PPG Signals
Compressed sensing exploits the sparsity of PPG signals in the frequency domain to reconstruct full-bandwidth waveforms from sub-Nyquist samples, enabling power-efficient data acquisition, wireless data compression, and recovery of PPG segments corrupted by motion artifacts.
How it works
Schematic summary of this guide. Waveforms are illustrative, not measured data.
PPG signals are approximately sparse in the frequency domain — the cardiac fundamental and 2–3 harmonics concentrate most signal energy in fewer than 10 spectral components. Compressed sensing theory guarantees exact recovery of -sparse signals from random measurements, far fewer than the Nyquist requirement.
Basis pursuit (L1 minimization) and greedy algorithms (OMP, CoSaMP) recover the sparse spectral representation from compressed measurements. Random sampling patterns or deterministic measurement matrices designed for PPG spectral structure optimize the compression-accuracy tradeoff.
Motion artifact recovery using compressed sensing treats corrupted PPG samples as missing data and reconstructs them using the sparse spectral model. By identifying artifact-corrupted samples (via SQI or accelerometer) and treating them as unobserved measurements, sparse recovery algorithms reconstruct clean PPG waveforms from the remaining clean samples.
Frequently Asked Questions
What compression ratio is achievable for PPG?
It depends on the use: heart-rate-only estimation tolerates more compression than morphology analysis, which loses detail as compression increases.
Does compressed sensing work for real-time PPG?
Signal acquisition is inherently real-time (random sub-sampling). Reconstruction algorithms (OMP, CoSaMP) are iterative but converge in 5–20 iterations, which can be feasible for near-real-time processing on embedded hardware.
How does PPG sparsity compare to ECG?
PPG is sparser than ECG in the frequency domain (smoother waveform, fewer harmonics) but less sparse in the wavelet domain (no sharp QRS complex). Frequency-domain compressed sensing is more effective for PPG, while wavelet-domain CS is more effective for ECG.