Source-linked AI summary
Photoplethysmography-Based Heart Rate Monitoring in Physical Activities via Joint Sparse Spectrum Reconstruction
Zhilin Zhang
TL;DR
Motion artifacts make PPG-based heart-rate estimation difficult during physical activity. JOSS jointly reconstructs PPG and acceleration spectra with an MMV sparse-recovery model, achieving low errors across 12 fast-running datasets sampled at 25 Hz.
Problem
Motion artifacts can overwhelm heartbeat-related PPG components during physical activity, making heart-rate estimation challenging.
Method
JOSS jointly estimates PPG and simultaneous acceleration spectra using the MMV model and a common sparsity constraint.
Results
1.28 ± 2.61 BPM average absolute estimation error was achieved across 12 datasets, versus 2.42 ± 2.47 BPM for TROIKA.
Takeaways & Limitations
The method simplifies motion-artifact removal and heart-rate peak tracking without an extra artifact-removal stage, supporting wearable implementation.
Abstract
from arXiv · showhide
Goal: A new method for heart rate monitoring using photoplethysmography (PPG) during physical activities is proposed. Methods: It jointly estimates spectra of PPG signals and simultaneous acceleration signals, utilizing the multiple measurement vector model in sparse signal recovery. Due to a common sparsity constraint on spectral coefficients, the method can easily identify and remove spectral peaks of motion artifact (MA) in PPG spectra. Thus, it does not need any extra signal processing modular to remove MA as in some other algorithms. Furthermore, seeking spectral peaks associated with heart rate is simplified. Results: Experimental results on 12 PPG datasets sampled at 25 Hz and recorded during subjects' fast running showed that it had high performance. The average absolute estimation error was 1.28 beat per minute and the standard deviation was 2.61 beat per minute. Conclusion and Significance: These results show that the method has great potential to be used for PPG-based heart rate monitoring in wearable devices for fitness tracking and health monitoring.
I. INTRODUCTION
PPG-based heart-rate monitoring is attractive for wearable devices but becomes difficult during physical activity because motion artifacts can overwhelm the heartbeat signal. JOSS addresses this challenge by jointly reconstructing PPG and acceleration spectra under a common sparsity constraint.
- I. INTRODUCTION: Motion artifacts from sensor-skin gaps and movement-related blood-flow changes can overwhelm heartbeat-related PPG components during physical activity.These artifacts make heart-rate estimation challenging.
- I. INTRODUCTION: Existing noise-reduction methods were mainly designed for scenarios in which motion artifacts are not strong.The cited methods include ICA, adaptive noise cancellation, spectrum subtraction, Kalman filtering, wavelet denoising, and empirical mode decomposition.
- I. INTRODUCTION: TROIKA targets extremely strong motion artifacts through signal decomposition, high-resolution spectrum estimation, and spectral peak tracking with verification.Its decomposition partially removes overlapping artifacts and sparsifies PPG spectra before peak selection.
- I. INTRODUCTION: JOSS jointly estimates PPG and simultaneous acceleration spectra using the MMV model, replacing TROIKA's SMV-based spectrum estimation.The shared spectral structure of the signals supplies the common sparsity constraint.
- I. INTRODUCTION: MMV theoretically offers better reconstruction than SMV at the same sparsity level and compression ratio.Acceleration spectra also expose motion-artifact peaks in corresponding PPG frequency bins.
- I. INTRODUCTION: Comparing PPG and acceleration spectral coefficients cleanses motion-artifact peaks, simplifying peak tracking and reducing processing stages for hardware implementation.The approach avoids TROIKA's signal decomposition and temporal-difference operations.
A. Motivations
The motivation for JOSS is that conventional sparse-spectrum processing and TROIKA's separate periodograms can leave motion artifacts in PPG spectra. Joint MMV reconstruction is proposed to improve artifact cleansing and spectrum estimation.
- A. Motivations: Sparse recovery models a raw PPG segment with a redundant DFT basis, a sparse solution vector, and a noise or modeling-error term.The estimated spectrum coefficient is obtained from the squared magnitude of the corresponding recovered coefficient.
- A. Motivations: Sparse spectrum estimation provides high resolution, low estimation variance, and greater robustness than conventional nonparametric and line-spectral methods.These are stated advantages of applying sparse signal recovery to spectrum estimation.
- A. Motivations: TROIKA first decomposes and differentiates PPG signals to suppress motion artifacts before sparse spectrum estimation and peak tracking.The decomposition only partially removes motion-artifact components.
- A. Motivations: Separate periodograms can place PPG and acceleration peaks from the same hand movement in nearby rather than identical frequency bins.The resulting artifact peak may remain in the later sparse-recovery PPG spectrum.
- A. Motivations: A dominant artifact peak near a previously selected heart-rate peak can remain in the PPG signal under the earlier procedure.This is identified as a second drawback of the signal-decomposition approach.
- A. Motivations: JOSS addresses these drawbacks by jointly estimating PPG and acceleration spectra with MMV-based sparse recovery, enabling reliable artifact-peak removal.The resulting cleansing is described as similar to spectral subtraction.
B. Joint Sparse Spectrum Reconstruction Using the MMV Model
The MMV model jointly reconstructs sparse spectra from PPG and simultaneous acceleration signals, exploiting row-wise common sparsity to align motion-artifact frequencies. This alignment supports accurate artifact removal and simplifies heart-rate peak identification.
- The MMV model jointly estimates spectra from PPG and simultaneous acceleration signals as multiple measurement vectors.Each solution-matrix column yields the spectrum of its corresponding signal; the experiments use one PPG channel and three acceleration channels.
- Row-wise sparsity aligns motion-artifact frequencies across PPG and acceleration spectra, enabling artifact peaks to be identified from acceleration signals.The common sparsity constraint assumes only a few rows of the solution matrix are nonzero.
- Regularized M-FOCUSS is selected because it offers fast speed and reliable performance when the redundant DFT basis is highly coherent.
- The MMV model can recover unique, less-sparse solutions and yield smaller errors than the SMV model under the same sparsity level and conditions.This helps address the many spectral coefficients caused by motion artifact in the pass band.
- The cleansed spectrum retained the heartbeat peak at the 112th frequency bin even when heartbeat and motion-artifact frequencies were close.The example reports that the heartbeat peak was accurately detected after joint reconstruction and spectral subtraction.
- Periodogram-based subtraction missed the heartbeat peak and left a false peak at the 116th bin, producing an error of about 5.9 BPM.
- The MMV-based approach simplifies heartbeat peak finding and avoids the signal decomposition and temporal-difference operations used in TROIKA.The paper states that this makes the approach more suitable for hardware implementation.
C. Spectral Subtraction
Spectral subtraction removes motion-artifact contributions by comparing acceleration and PPG spectral coefficients at corresponding frequency bins, then thresholding the processed spectrum.
- Spectral subtraction begins by taking the maximum acceleration spectral coefficient at each frequency bin.
- The maximum acceleration coefficient is subtracted from the PPG coefficient at the same frequency bin to obtain a processed PPG spectrum.
- Coefficients below pmax/4 are set to zero to produce the cleansed PPG spectrum.
- The PPG and acceleration segments are normalized to have the same variance, or energy, before subtraction.
D. Spectral Peak Tracking
The proposed spectral peak tracker uses overlapping time windows and prior heart-rate estimates to follow the current peak with fewer tuning parameters.
- The tracker relies on the observation that heart-rate values in heavily overlapping successive windows are very close.
- The tracking procedure has four stages: initialization, peak selection, peak verification, and peak discovery.
- During initialization, wearers reduce hand motions for several seconds and heart rate is estimated from the highest PPG spectral peak.
1) Initialization:
Initialization detects sufficiently reduced hand motion using spectral kurtosis, while peak selection searches around the previous estimate and expands the range when necessary.
- Initialization: Spectral kurtosis from 0.8 Hz to 2.5 Hz classifies whether hand motions have been reduced sufficiently.A kurtosis value larger than 10 identifies the current window as initialization.
- Initialization: Initialization selects the highest PPG spectral peak in the 0.8–2.5 Hz range.
- Peak Selection: Peak selection first searches a range centered on the previously estimated heart-rate frequency bin, R1 = [prevLoc−∆1, prevLoc+∆1].
- Peak Selection: If R1 contains peaks, the tracker chooses the one closest to the previous location; otherwise it expands to R2 and selects the highest peak if available.
- Peak Selection: When two candidate peaks are equally distant, an Smoother applied to at least 10 prior estimates predicts whether heart rate should increase or decrease.
- Peak Verification: The selected peak is represented by its frequency bin curLoc and associated BPM value curBPM, before verification checks for motion-artifact selection.
3) Peak Verification:
Peak verification checks whether a selected spectral peak is plausible from one time window to the next, and triggers peak discovery when the tracked peak appears lost.
- Peak Verification: A difference exceeding 12 BPM between current and previous estimates flags the selected spectral peak as likely incorrect.The current location and BPM are reset to the previous values.
- Peak Verification: Repeatedly selecting the same spectral location indicates that the target heartbeat peak may have been lost.This condition triggers a peak-discovery procedure.
- Peak Discovery: Peak discovery predicts the heartbeat’s spectral location from the macro-trend of the K previously estimated HR values.It uses a larger smoothing parameter and search range than peak selection because the exact HR location is more uncertain.
- Datasets: The evaluation used 12 PPG datasets containing wrist PPG, three-axis acceleration, and simultaneously recorded ECG signals.The datasets came from 12 healthy male subjects, and ECG-derived HR provided the evaluation ground truth.
- Datasets: Signals were recorded during treadmill walking or running, with PPG and acceleration downsampled from 125 Hz to 25 Hz for the experiments.The protocol included speeds from 1–2 km/hour to 12–15 km/hour.
B. Experimental Settings
The experiments estimated HR in sliding windows after filtering, then evaluated estimates with absolute-error, percentage-error, Bland–Altman, and correlation measures.
- Experimental Settings: HR was estimated in 8-second windows that advanced by 2 seconds over simultaneous PPG and acceleration signals.This windowing procedure was applied before JOSS processing.
- Experimental Settings: Raw signals were bandpass filtered from 0.4 Hz to 4 Hz using a second-order Butterworth filter before JOSS.Regularized M-FOCUSS used p = 0.8, λ = 10^-10, and N = 1024, with at most four iterations.
- Experimental Settings: Peak tracking used Δ1 = 15, Δ2 = 25, and Δ3 = 30, with stage-specific smoothing parameters and thresholds.The Peak Selection Stage used smoothing 5 and H = 10; Peak Discovery used smoothing 20 and K = 30.
- Performance Measurement: Ground-truth HR was calculated by manually identifying ECG R-peaks in each time window, avoiding algorithmic R-peak detection errors.The ECG signals were sampled at 125 Hz.
- Performance Measurement: Performance included average absolute error, average absolute error percentage, Bland–Altman limits of agreement, and Pearson correlation.The limits of agreement were defined as [μ − 1.96σ, μ + 1.96σ].
D. Results
Across 12 datasets sampled at 25 Hz, JOSS outperformed TROIKA on absolute-error measures and showed close agreement with ground-truth HR in representative and aggregate analyses.
- Results: 1.28 ± 2.61 BPM was JOSS’s average absolute estimation error across the 12 datasets.TROIKA’s corresponding Error1 was 2.42 ± 2.47 BPM.
- Results: 1.01% ± 2.29% was JOSS’s average absolute error percentage, compared with TROIKA’s 1.82% ± 2.07%.Both metrics were computed after excluding specified initial segments with strong motion artifact.
- Results: The t-test found JOSS’s absolute estimation error significantly smaller than TROIKA’s at α = 0.01, with p = 6.3 × 10^-39.The comparison used errors from individual estimates across the 12 datasets.
- Results: On Dataset 8, JOSS’s estimated HR trace was almost the same as ground-truth, whereas TROIKA sometimes produced errors.Dataset 8 was selected randomly for the trace comparison.
- Results: The aggregate Bland–Altman limits of agreement were [−5.94, 5.41] BPM, and Pearson correlation was 0.993.The fitted line relating estimates to ground truth was y = 0.991x + 0.432.
IV. DISCUSSIONS
The experiments use averaged heart-rate comparisons because beat-to-beat correspondence weakens during movement, while performance evaluation is limited to one skin-color and LED-light combination.
- The experiments used yellow-skinned subjects and green LED light, so performance under other skin colors and LED lights remains future work.Skin color and LED light are identified as factors affecting PPG characteristics and algorithm performance.
- PPG pulse-to-pulse intervals correlate less strongly with ECG beat-to-beat intervals during movement, so the study compares averaged ground-truth and estimated heart rates.Ground-truth HR uses ECG over an 8-second window, while estimated HR comes from the PPG spectrum in the same window.
- y = 0.991x + 0.432, with R2 = 0.986 and Pearson correlation = 0.993, summarizes estimates against ground-truth values across 12 datasets.
B. Advantages and Possible Improvement Approaches of JOSS
JOSS performs well at low sampling rates and simplifies motion-artifact handling through joint sparse reconstruction, while several extensions could improve robustness or estimation accuracy.
- Advantages: JOSS works well at low sampling rates, potentially reducing acquisition and wireless-transmission energy consumption and extending wearable-device battery life.
- Possible Improvement Approaches: Gridless joint spectral compressed sensing could reduce errors caused when heart-rate frequencies fall between frequency-grid points.
- Possible Improvement Approaches: Smoothing estimated heart-rate traces may help when strict real-time operation is not required because effective smoothing algorithms are often offline.
- Possible Improvement Approaches: Adding a noise-removal module can improve JOSS robustness to motion artifact, but increases processing time, power consumption, and circuit-design complexity.
- Advantages: The MMV model exploits common spectral sparsity between PPG and acceleration signals, avoiding an extra noise-removal stage and simplifying the algorithm.