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TROIKA: A General Framework for Heart Rate Monitoring Using Wrist-Type Photoplethysmographic Signals During Intensive Physical Exercise
Zhilin Zhang, Zhouyue Pi, Benyuan Liu
TL;DR
Intensive exercise makes wrist-type PPG heart-rate monitoring difficult because strong motion artifacts interfere with the signals. TROIKA combines signal decomposition, sparse signal reconstruction, and verified spectral peak tracking, achieving a 2.34 BPM average absolute error and 0.992 Pearson correlation on fast-running recordings from 12 subjects.
Problem
Wrist-type PPG heart-rate monitoring during intensive exercise is difficult because strong motion artifacts interfere with the signals.
Method
TROIKA combines signal decomposition for denoising, sparse signal reconstruction for high-resolution spectrum estimation, and spectral peak tracking with verification.
Results
2.34 BPM average absolute error and 0.992 Pearson correlation were obtained on recordings from 12 subjects running at a peak speed of 15 km/hour.
Takeaways & Limitations
TROIKA provides a flexible framework whose three parts are each indispensable to its reported high performance and whose variants can suit hardware requirements in wearable devices.
Abstract
from arXiv · showhide
Heart rate monitoring using wrist-type photoplethysmographic (PPG) signals during subjects' intensive exercise is a difficult problem, since the signals are contaminated by extremely strong motion artifacts caused by subjects' hand movements. So far few works have studied this problem. In this work, a general framework, termed TROIKA, is proposed, which consists of signal decomposiTion for denoising, sparse signal RecOnstructIon for high-resolution spectrum estimation, and spectral peaK trAcking with verification. The TROIKA framework has high estimation accuracy and is robust to strong motion artifacts. Many variants can be straightforwardly derived from this framework. Experimental results on datasets recorded from 12 subjects during fast running at the peak speed of 15 km/hour showed that the average absolute error of heart rate estimation was 2.34 beat per minute (BPM), and the Pearson correlation between the estimates and the ground-truth of heart rate was 0.992. This framework is of great values to wearable devices such as smart-watches which use PPG signals to monitor heart rate for fitness.
I. INTRODUCTION
Wrist-type PPG enables wearable heart-rate monitoring but is strongly affected by motion artifacts during intensive exercise. TROIKA addresses this setting with decomposition, sparse reconstruction, and verified spectral tracking, achieving low error on fast-running data.
- HR monitoring helps exercisers control training load and is a key feature in wrist-worn wearable devices.
- Existing motion-artifact techniques mainly target small motions or slower running with fingertip or ear recordings, limiting their demonstrated relevance to intensive wrist-based exercise.
- Wrist-based PPG experiences stronger, more complicated motion artifacts than fingertip or earlobe measurements, despite its wearable-device advantages.
- TROIKA combines signal decomposition, sparse signal reconstruction, and spectral peak tracking with verification for heart-rate monitoring during intensive physical activity.Decomposition denoises and sparsifies the signal, reconstruction estimates a high-resolution spectrum, and verification helps reject motion-artifact interference.
- 2.34 beat per minute (BPM) average absolute error was obtained on recordings from 12 subjects running at a peak speed of 15 km/hour.
II. PROBLEM STATEMENT AND MOTIVATIONS
Strong motion artifacts make wrist-PPG heart-rate estimation difficult because conventional spectral methods can smear or obscure the heart-rate peak. TROIKA addresses this with denoising, high-resolution spectrum estimation, and spectral peak tracking.
- When motion artifacts are strong, time-domain heart-rate estimation is difficult and Periodogram can produce high-variance spectra with serious leakage.Leakage from a dominant artifact peak may smear a nearby weak heart-rate peak.
- Sparse signal reconstruction offers higher resolution, lower variance, and greater robustness than nonparametric spectrum estimation, without requiring model-order selection.It requires preprocessing because motion-artifact-contaminated PPG spectra may not be sparse.
- A large pulse-oximeter-to-skin gap can bury the heart-rate peak in random spectral fluctuations, and the peak may disappear entirely in extreme cases.These cases require methods for peak selection and verification beyond high-resolution spectrum estimation.
- TROIKA combines signal decomposition for denoising and spectral sparsification, sparse signal reconstruction for high-resolution estimation, and spectral peak tracking.The framework estimates heart rate from a single-channel PPG signal with simultaneously recorded acceleration data in sliding time windows.
A. Signal Decomposition
TROIKA uses signal decomposition to separate PPG components, identify motion-related components using acceleration frequencies, and reconstruct a cleansed signal before sparse spectrum estimation.
- Signal decomposition represents a signal as multiple components and reconstructs grouped components into separate time series.The procedure comprises embedding, SVD, grouping, and reconstruction when SSA is used.
- The remaining decomposed PPG time series are reconstructed as a cleansed signal after identified noise and interference components are removed.The decomposition approach can be varied; SSA is selected for the experiments.
- SSA partially removes motion-artifact components from 0.4 Hz to 5 Hz and sparsifies the spectrum in that range for sparse signal reconstruction.Artifact frequencies outside the band are removed by bandpass filtering beforehand.
- Acceleration spectra identify dominant motion frequencies, whose corresponding PPG components are removed during reconstruction.Dominant frequencies are selected when spectral-peak amplitude exceeds 50% of the maximum in an acceleration spectrum.
- Heartbeat-related frequency neighborhoods are excluded from the acceleration-frequency set to reduce the risk of removing heartbeat components.The refined set uses prior-window estimates of heartbeat fundamental and harmonic frequencies.
B. Temporal Difference Operation
TROIKA temporally differentiates the cleansed PPG signal before sparse spectrum estimation to emphasize periodic heartbeat structure and suppress random fluctuations.
- TROIKA differentiates the SSA-cleansed PPG signal before applying sparse signal reconstruction for improved robustness.The experiments use the second-order difference.
- Temporal differentiation preserves the fundamental and harmonic frequencies of a periodic heartbeat signal.First- and second-order differences retain these frequencies when the differentiation order is not large.
- Because heartbeat is approximately periodic while motion artifacts are generally aperiodic in short windows, differentiation makes heartbeat peaks more prominent.The operation suppresses random spectral fluctuations, with exceptions for rhythmic hand-swing artifacts.
C. SSR
SSR estimates a high-resolution spectrum by recovering a sparse solution from an observed signal and known basis matrix. In TROIKA, preprocessing is important because motion artifacts can make the PPG spectrum non-sparse and undermine SSR.
- SSR model: SSR models the observed signal using a known basis matrix, a sparse solution vector, and an unknown noise vector.The objective is to find the sparsest solution consistent with the observation and basis matrix.
- Spectrum estimation: The recovered coefficients produce a sparse power spectrum through sk = |bxk|2.The k-th spectrum element is defined from the squared magnitude of the corresponding recovered coefficient.
- Preprocessing: Bandpass filtering restricts the retained spectrum to coefficients associated with the 0.4 Hz to 5 Hz signal band.Frequency-bin pruning can reduce the computational load before SSR.
- Algorithm choice: FOCUSS was chosen because it is robust when the basis-matrix columns are highly correlated.The framework is not restricted to a specific SSR algorithm, but algorithm choice can affect performance.
- Sparsity requirement: SSR performance degrades when the solution is not sparse, so signal decomposition and temporal differencing help sparsify motion-contaminated PPG spectra.The preprocessing procedures are described as important for alleviating the effects of complicated hand movements.
- Sparsity requirement: Bandpass filtering alone may be insufficient because correlated basis columns make even a small number of nonzero coefficients difficult for SSR.The paper therefore prefers further removal of significantly nonzero coefficients associated with motion artifacts.
- Resolution trade-off: Choosing a larger N reduces off-grid effects but increases basis-column correlation, creating a trade-off for SSR performance.The experiments used N = 4096, with each grid corresponding to about 1 BPM.
D. Spectral Peak Tracking
Spectral peak tracking uses harmonic relationships and temporal continuity of heart-rate peaks to select the HR-related spectral peak. The tracking procedure comprises initialization, peak selection, and verification.
- Tracking rationale: Spectral peak tracking exploits HR harmonic relationships and the closeness of HR values in largely overlapping successive windows.Experiments found that the HR-associated peak often remains at the same location across successive windows.
- Procedure: The tracking procedure consists of initialization, peak selection, and verification.
- Initialization: Initialization requires wearers to reduce hand motions for 2 or 3 seconds so HR can be estimated from the highest PPG spectral peak.Without initialization, multiple spectral peaks provide no prior information for identifying the correct HR peak.
1) Initialization:
After initialization, TROIKA searches near the previous HR peak and its first harmonic, then uses harmonic relations or temporal continuity to select a candidate peak.
- Peak selection: The current search range for the HR fundamental is centered on the previous peak location with Δs = 16 in the experiments.A corresponding search range is also defined for the first-order harmonic.
- Peak selection: The selected peak is represented by its frequency-location index, while candidate peaks are identified in the fundamental and harmonic search ranges.
- Peak selection: When a peak pair has a harmonic relation, the fundamental-range peak is treated as the HR frequency location.
- Peak selection: If no harmonic peak pair exists because of motion artifacts, selection relies on the observed continuity of the peak location across successive windows.
- Peak selection: The method includes a fallback case for situations in which no peaks are found in either search range.
- Indexing: The first frequency bin corresponds to 0 Hz, so harmonic-index calculations use an offset before converting locations.
- Verification: Verification is necessary because peak selection can incorrectly follow motion-artifact peaks or spectral fluctuations.
3) Verification:
Verification regularizes implausibly large changes between successive BPM estimates and broadens the search when prolonged interference causes tracking to stagnate.
- Change regularization: 10 BPM is the threshold for regularizing a large change between successive estimated BPM values.The paper states that successive-window changes rarely exceed 10 BPM.
- Change regularization: θ = 6 corresponds to about 11 BPM with N = 4096 over the [0, 125] Hz spectrum, and τ may be set to 2.The regularized peak location is adjusted relative to the previous location when the selected change exceeds the threshold.
- Long-term tracking: If the selected peak remains unchanged for h successive windows during strong interference, the HR peak may be lost and not recovered.
- Trend estimation: The trend direction is determined from the predicted and previous BPM values using a ±3 BPM threshold.The predicted BPM comes from third-order polynomial fitting over the previous 20 windows.
E. Remarks
TROIKA is presented as a general framework whose specific signal-decomposition and sparse-reconstruction algorithms can be replaced. Its parameter settings were tested for robustness under the experiment’s sampling-rate conditions.
- TROIKA can use alternative algorithms, including sparse Bayesian learning instead of FOCUSS and EMD instead of SSA.
- TROIKA’s user-defined parameter values were selected heuristically, and its performance was robust to other tested values.
- The parameter settings were based on a sampling rate of fs = 125 Hz and should be adjusted proportionally when the sampling rate changes substantially.For fs = 25 Hz, the frequency-bin count N should be about one-fifth of its original value.
- The experiments used recordings from 12 male subjects aged 18–35, with wrist PPG, wrist acceleration, and ECG recorded simultaneously.
- Regularized M-FOCUSS used p = 0.8, λ = 0.1, N = 4096, and five iterations in the experiments.
C. Performance Measurement
Performance was evaluated against ECG-derived heart-rate ground truth using error, agreement, and correlation measures across 12-subject recordings. The complete TROIKA framework achieved low error and high correlation, while removing any main component reduced robustness.
- Ground-truth heart rate was calculated from simultaneous ECG by dividing 60 times the cardiac-cycle count H by window duration D.
- 2.34 ± 0.82 BPM was the average absolute estimation error, while the average error percentage was 1.80% across 12 subjects.
- 0.992 was the Pearson correlation coefficient between TROIKA estimates and ground-truth heart rate.
- The Bland–Altman analysis produced limits of agreement of [−7.26, 4.79] BPM, with standard deviation σ = 3.07 BPM.
- Removing signal decomposition, replacing SSR with FFT, or removing spectral peak verification made performance non-robust, with complete HR-tracking loss on some datasets.
- On Subject 5 recordings, the complete framework estimated the ground-truth trace closely, including small heart-rate changes.
- SSA partially reduced motion artifacts, helping expose the heart-rate spectral peak in the processed PPG example.
- Performance remained almost unchanged across the tested values of L, Δ, τ, and Δs.
E. Discussions
TROIKA showed strong and competitive performance for heart-rate monitoring during running, while retaining flexibility for wearable-device requirements. The authors also note that lower sampling rates can reduce computational load with nearly unchanged estimation performance.
- E. Discussions: 0.992 Pearson correlation and 3.07 BPM standard deviation of error demonstrate TROIKA’s performance during running.Prior studies reported Pearson correlations of 0.75, 0.78, and 0.64, while another reported an 8.7 BPM standard deviation of error.
- E. Discussions: Reducing the sampling rate to 25 Hz and suitably tuning parameters produced nearly unchanged heart-rate estimation performance while dramatically shortening running time.The authors identify this as a topic for future investigation.
- E. Discussions: Each of TROIKA’s three parts is indispensable to its high performance.The three parts are signal decomposition, sparse signal reconstruction, and spectral peak tracking with verification mechanisms.
- E. Discussions: Many TROIKA variants can be derived by selecting algorithms in its three parts according to hardware-design requirements.This flexibility is presented as valuable for wearable devices.