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.
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 K-sparse signals from M ≥ O(K·log(N/K)) random measurements, far fewer than the Nyquist requirement. For PPG with K ≈ 5–8 significant spectral components, 20–40% of Nyquist-rate samples suffice for accurate reconstruction.
Basis pursuit (L1 minimization) and greedy algorithms (OMP, CoSaMP) recover the sparse spectral representation from compressed measurements. For PPG data compression in wireless body sensor networks, compressed sensing reduces data transmission by 50–75% while maintaining <3% reconstruction error (NRMSE), extending battery life proportionally. 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. This approach achieves 2–5 bpm HR estimation accuracy during moderate motion from only 30–50% of samples.
Frequently Asked Questions
What compression ratio is achievable for PPG?
Ratios of 2:1 to 4:1 (25–50% of Nyquist samples) typically maintain clinically acceptable reconstruction quality. Higher compression (10:1) is possible for HR-only estimation but loses morphological detail.
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, feasible for near-real-time processing on embedded hardware with 50–200 ms latency.
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.