⚡ electrical engineering

BLiSS: A Beat-Local, Signal-Quality-Informed Kalman Smoother for ECG Denoising under Non-Stationary Muscle Artifact, with Ectopic-Beat Reconstruction Assessment

The paper proposes BLiSS, a beat-local, signal-quality-informed Kalman smoother that outperforms existing methods in denoising ECG signals under non-stationary muscle artifacts while effectively preserving the morphology of ectopic beats, although some limitations remain in whole-beat and P-wave preservation.

Original author: Khanh Duy Tran

Published 2026-11-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original author: Khanh Duy Tran

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the author. For technical accuracy, refer to the original paper. Read full disclaimer

The human heart speaks in a language of electricity, sending tiny, rhythmic pulses through the body that doctors can capture on a strip of paper or a digital screen. This recording, known as an electrocardiogram, is a vital tool for spotting irregularities in the heartbeat, from skipped beats to dangerous arrhythmias. However, the signal is fragile. When a person moves, their muscles generate electrical noise that overlaps with the heart's own rhythm, much like static on a radio station. This interference, called muscle artifact, can blur the sharp lines of the heartbeat, making it difficult to distinguish a normal beat from a dangerous one. The challenge for engineers is to clean up this noisy signal without accidentally smoothing out the very irregularities they are trying to find, because those irregularities are often the most important part of the story.

A researcher named Khanh Duy Tran has developed a new method to solve this problem, aiming to strip away the muscle noise while keeping the unique shape of abnormal heartbeats intact. The approach, named BLiSS, treats every single heartbeat as its own distinct event rather than assuming all beats look the same. In standard cleaning methods, algorithms often try to guess what a beat should look like based on the beats that came before it. This works well for a steady, regular rhythm, but it fails when the heart skips a beat or fires early, because the algorithm tries to force the abnormal beat into a normal shape. Tran's method avoids this trap by assessing the quality of the raw signal for each individual beat and adjusting its cleaning strength accordingly. It uses a mathematical smoothing technique that looks both forward and backward in time within the beat, refining the shape based on the actual data present in that specific moment.

To test this idea, the researcher applied the new method to a large collection of heart recordings that had been artificially contaminated with different types of muscle noise. These recordings came from a well-known database containing approximately 22 hours of heart data from dozens of patients, including many who had irregular beats. The noise added to these recordings varied from a constant hum to sudden bursts of static, mimicking the unpredictable way muscles interfere with a real-world recording. The new method was compared against several other existing techniques, including those that rely on complex mathematical models of heart dynamics and others that focus specifically on removing muscle noise. The goal was to see which method could raise the clarity of the signal the most while preserving the true shape of the abnormal beats.

The results showed that the new method, BLiSS, was the most effective at cleaning the signal overall. Across all the different types of noise tested, it improved the clarity of the heart signal by an average of between 4.44 and 5.38 decibels, a larger gain than any of the other methods. This improvement was particularly noticeable when the noise changed suddenly, such as when a burst of muscle activity interrupted a quiet recording. More importantly, the method excelled at protecting the shape of the abnormal beats. When the researchers looked specifically at premature ventricular contractions, which are early, wide heartbeats that can signal heart trouble, the new method produced the smallest error in reconstructing their shape. It also did the best job at preserving the height of these abnormal beats, a critical detail for doctors assessing the severity of the condition.

While the new method was superior at cleaning the main part of the abnormal beat, the study found that it was not perfect in every single area. Another method, which used a different combination of filters, actually did a slightly better job at preserving the entire length of the abnormal beat and at pinpointing the timing of the very first electrical wave in the heart for a specific group of patients. This suggests that no single tool is perfect for every situation, but the new approach offers a significant advantage in the most critical area: distinguishing the true shape of a dangerous beat from the noise that surrounds it. The study also tested what would happen if the algorithm tried to use information from the previous beat to guess the current one, a common strategy in other systems. The results showed that doing so actually made the reconstruction of abnormal beats worse, confirming that treating each beat as a unique event is the better path.

The research concludes that by focusing on the quality of the signal within each individual beat and avoiding assumptions about what the beat should look like, it is possible to remove muscle noise more effectively than before. This approach allows the heart's true voice to be heard even when the body is moving and the signal is under attack. While the method still has limitations, such as needing further testing on recordings from wearable devices in real-world settings, it represents a meaningful step forward in making heart monitoring more reliable. The findings suggest that the key to cleaning these signals lies not in forcing them to fit a standard pattern, but in listening carefully to the unique story each beat tells.

Technical Summary: BLiSS for ECG Denoising

Problem Statement
Electrocardiogram (ECG) recordings are frequently corrupted by non-stationary muscle artifacts (MA), which spectrally overlap with cardiac activity, making noise suppression difficult without distorting the underlying waveform. A critical challenge in this domain is preserving the morphology of ectopic beats (such as Premature Ventricular Contractions [PVCs] and Supraventricular Ectopic Beats [SVEBs]), which often deviate significantly from normal beat shapes. Existing methods often rely on dominant beat morphology priors or segment-level signal quality indices that fail to adapt to rapid, beat-to-beat changes in noise levels. Furthermore, standard evaluations often aggregate performance across entire recordings, potentially obscuring reconstruction errors specific to less frequent ectopic beat types.

Methodology: The BLiSS Framework
The author proposes BLiSS (Beat-Local, Signal-Quality-Informed Kalman Smoother), a state-space smoothing algorithm designed to handle non-stationary MA while preserving ectopic morphology. The framework operates through five sequential modules:

Fixed Wavelet-Wiener Front End: The raw ECG signal ( $z[n]$ ) undergoes baseline wander and mains interference removal via high-pass and band-stop filters. A two-stage Wavelet-Wiener Filter (WWF) then produces an initial pilot estimate ( $y[n]$ ). This stage uses stationary wavelet transforms with non-negative garrote thresholding and pilot-derived Wiener gains.
R-Peak Detection and Beat Extraction: An R-peak detector (XQRS) identifies beat locations on the WWF output. For each detected R-peak ( $\tau_k$ ), a fixed window ($0.30$ s pre-peak to $0.70$ s post-peak) is extracted. A linear baseline is estimated and subtracted to produce a baseline-corrected observation beat ( $\tilde{o}_k$ ).
Raw-Beat Quality Assessment ( $R_k$ ): Crucially, the algorithm assesses the quality of the raw ECG beat (before WWF filtering) to determine the measurement variance ( $R_k$ ) for the Kalman filter. $R_k$ is calculated based on the beat's total power ( $P_k$ ) and the fraction of high-frequency power ( $h_k$ ) within the 40–125 Hz band. This allows the measurement uncertainty to vary dynamically on a beat-by-beat basis, reflecting the instantaneous contamination level.
Beat-Local State-Space Smoothing:
- State Model: A constant-velocity model describes the waveform amplitude and its rate of change.
- Initialization: The process noise intensity ( $q$ ) is estimated once per recording run using Maximum Likelihood on the first 10 beats. Each beat is initialized independently without transferring morphology priors from preceding beats.
- Filtering: A forward Kalman filter processes the beat, followed by a backward Rauch–Tung–Striebel (RTS) smoother. The measurement variance $R_k$ (derived from raw-beat quality) modulates the smoothing strength for that specific beat.
Continuous Reconstruction: The denoised beat windows are stitched together. In overlapping regions, the window starting later supplies the output samples. The removed baseline is restored to generate the final continuous signal.

Key Contributions

Novel Algorithm: The introduction of BLiSS, which integrates fixed wavelet-Wiener filtering with beat-local, signal-quality-informed state-space smoothing. It uniquely avoids imposing a preceding-beat morphology prior, allowing for the reconstruction of abrupt morphological changes typical of ectopic beats.
Comprehensive Benchmarking: A controlled evaluation across all 44 non-paced recordings of the MIT-BIH Arrhythmia Database, contaminated with muscle artifact from the MIT-BIH Noise Stress Test Database under four distinct profiles: constant-level, step, burst, and alternating.
Targeted Ectopic Assessment: A specific evaluation protocol quantifying reconstruction fidelity for PVCs and SVEBs under event-overlapping bursts. This includes regional (QRS) and whole-beat error metrics, as well as PVC amplitude preservation, addressing a gap in previous studies that relied solely on aggregate recording-level metrics.
Ablation Studies: Systematic analysis of the algorithm's components, demonstrating the necessity of beat-specific measurement weighting and backward smoothing, and showing that adding a preceding-beat prior actually increases ectopic reconstruction errors.

Results

Continuous Denoising: BLiSS achieved the highest average Signal-to-Noise Ratio (SNR) gain across all four contamination profiles (ranging from 4.44 dB to 5.38 dB). It outperformed three Kalman-based methods (AKFB, HKF, ADAEKF-AR3) and two EMG-focused methods (IRM, AWWF + AMAF). The margin over the closest competitor (AWWF + AMAF) was most significant under step and burst noise conditions.
Ectopic Beat Reconstruction:
- PVCs: BLiSS achieved the lowest mean QRS-region Normalized Root-Mean-Square Error (NRMSE: 0.217) and the lowest PVC QRS amplitude Mean Absolute Error (0.194 mV) among all tested methods.
- SVEBs: BLiSS achieved the lowest QRS-region NRMSE (0.241). However, for whole-beat SVEB reconstruction, the AWWF + AMAF method achieved a lower NRMSE (0.501 vs. 0.596 for BLiSS).
- Timing: In a small atrial subgroup, AWWF + AMAF, ADAEKF-AR3, and IRM demonstrated lower P-peak timing errors than BLiSS.
Ablation Findings: Removing beat-specific weighting (using a fixed $R$ ) reduced SNR gain by approximately 0.5–0.8 dB and increased ectopic errors. Adding a preceding-beat morphology prior preserved overall SNR but significantly increased PVC and SVEB reconstruction errors, confirming that prior-based models can hinder the preservation of non-standard beat morphologies.

Significance and Claims
The paper claims that BLiSS successfully balances noise suppression with the preservation of ectopic beat morphology, achieving the highest mean denoising gain and the lowest mean QRS-region errors for both PVCs and SVEBs. The author emphasizes that their results highlight a trade-off: while BLiSS excels at preserving the critical QRS region of ectopic beats, other methods (specifically AWWF + AMAF) may perform better on whole-beat reconstruction or P-wave timing in specific contexts.

The study concludes that overall denoising gain alone is insufficient to guide model selection when ectopic-beat preservation is a priority. The author asserts that their targeted assessment reveals class-specific filtering behaviors that aggregate metrics often obscure. They acknowledge limitations, including the heuristic setting of parameters, the use of fixed windows that may not cover all atypical complexes, and the reliance on synthetic noise injection rather than naturally occurring artifacts in wearable devices. Future work is proposed to evaluate the method on naturally contaminated wearable recordings and to incorporate neighboring beat information while strictly preserving abrupt morphological changes.

Technical Summary: BLiSS for ECG Denoising

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