⚡ electrical engineering

A New Non-Negative Matrix Factorization Approach for Blind Source Separation of Cardiovascular and Respiratory Sound Based on the Periodicity of Heart and Lung Function

This paper proposes a modified affine non-negative matrix factorization approach that leverages the periodic properties of heart and lung signals to effectively blind-separate cardiovascular and respiratory sounds from noisy digital stethoscope recordings, demonstrating improved performance metrics compared to existing methods.

Original authors: Yasaman Torabi, Shahram Shirani, James P. Reilly

Published 2026-05-27

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CC BY 4.0

Original authors: Yasaman Torabi, Shahram Shirani, James P. Reilly

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

Imagine you are standing in a busy kitchen. On one stove, a pot of soup is bubbling rhythmically (that's the heart). On the other, a kettle is whistling with a longer, more drawn-out sound (that's the lungs). Now, imagine someone records the entire kitchen with a single microphone. The result is a messy audio file where the bubbling and whistling are mixed together, making it hard to hear either one clearly.

This is exactly the problem doctors face when listening to a patient's chest. The heart and lungs make sounds at the same time, and their frequencies overlap, creating a "kitchen noise" that is difficult to untangle.

This paper presents a new digital tool to solve this problem. Here is how it works, broken down into simple concepts:

1. The Goal: Unmixing the Soup

The researchers wanted to take that messy recording and separate it back into two clean tracks: one for just the heart and one for just the lungs. This is called Blind Source Separation. They call it "blind" because the computer doesn't know what the original sounds looked like; it has to figure it out just by listening to the mix.

2. The Old Way vs. The New Way

Previous methods tried to separate these sounds using standard math tricks, but they often left behind "ghosts" of the other sound (like hearing a faint whistling in the heart track).

The authors propose a new approach based on Non-Negative Matrix Factorization (NMF). Think of NMF as a very smart puzzle solver. It looks at the messy audio and tries to break it down into two basic building blocks:

The Pattern (A): What the heart sound usually looks like.
The Pattern (X): What the lung sound usually looks like.

3. The Three Secret Ingredients

The authors didn't just use a standard puzzle solver; they built a custom machine with three special upgrades:

The "Scale and Offset" Knob:
Heart sounds are quiet and sharp; lung sounds are louder and slower. Standard math struggles with this difference. The authors added a special "scale and offset" block. Imagine this as a pair of glasses that adjusts the brightness and contrast of the image. It stretches the quiet heart sounds and compresses the loud lung sounds so the math can handle them equally well.
The "Two-Track" Factory (Parallel Structure):
Instead of using one machine to try to find both sounds at once, they built two separate machines running side-by-side.
- Machine A is tuned specifically to hunt for the heart.
- Machine B is tuned specifically to hunt for the lungs.
  This is like having two detectives in a room: one only looks for red cars, and the other only looks for blue trucks. They don't get confused with each other, leading to a much cleaner result.
The "Rhythm" Detector (Periodicity):
This is the most clever part. The heart beats in a fast, regular rhythm (like a drum). The lungs breathe in a slower, different rhythm (like a wave).
The new algorithm doesn't need to know exactly how fast the heart beats beforehand. Instead, it listens to the output of both machines and asks: "Which one has the fast, steady drumbeat?" That one is the heart. "Which one has the slow wave?" That one is the lungs. It uses the natural rhythm of the body to decide which sound goes where.

4. The Results

The team tested this on 100 different "kitchen recordings" (synthesized mixes of real heart and lung sounds). They compared their new tool against other popular methods.

The results showed that their new method was much better at cleaning up the noise. Specifically:

It reduced the "interference" (the other sound leaking through) significantly.
It produced a clearer, more accurate separation of the two sounds than previous methods.

Summary

In short, the authors built a smarter digital stethoscope software. Instead of just guessing how to separate the sounds, they created a system that uses two specialized teams working in parallel, adjusts the volume automatically, and uses the natural rhythm of the heart and lungs to ensure the right sound ends up in the right file. This makes it easier for doctors to hear exactly what is happening inside a patient's chest.

Technical Summary: A New Non-Negative Matrix Factorization Approach for Blind Source Separation of Cardiovascular and Respiratory Sounds

Problem Statement
Cardiac and respiratory auscultation provides critical diagnostic information for cardiovascular and respiratory diseases. However, the clinical utility of auscultation is often hindered by the challenge of noise and signal interference. Heart sounds (cardiac) and lung sounds (respiratory) frequently overlap in the frequency domain and interact physically, making it difficult to extract pure acoustic signals from a single recording. While Blind Source Separation (BSS) techniques exist, standard methods like Independent Component Analysis (ICA) often require prior knowledge regarding source statistics (mean and variance), and existing Non-Negative Matrix Factorization (NMF) applications for bioacoustics have struggled with noise contamination and the separation of mixed-sign signals. Furthermore, many existing approaches rely on manual segmentation or specific prior knowledge of signal periods, limiting their automation and robustness.

Methodology
The authors propose a modified NMF approach designed to blindly separate heart and lung sounds recorded by a digital stethoscope. The methodology integrates several distinct technical components:

Pre-processing: The input signals undergo bandpass filtering (50–250 Hz for heart, 60–300 Hz for lung) and normalization to mitigate noise and standardize amplitude.
Modified Affine NMF: The core algorithm utilizes an $\alpha$ -NMF framework minimizing $\alpha$ -divergence. To address the limitation of standard NMF in recovering mixed-sign signals, the authors introduce a "scale-and-offset" block. This modification includes an adjustable offset term ( $\lambda_2$ ) to ensure non-negativity and distinct scaling factors ( $\lambda_1$ ) for heart and lung detection blocks. This allows the algorithm to handle the mixed-sign nature of the raw acoustic data while leveraging biological priors (e.g., lung sounds being slower and more dominant than heart sounds).
Multilayer Parallel Structure: Unlike traditional single-module NMF, the proposed system employs a parallel structure with two separate NMF modules. One module is tuned to extract heart sounds, and the other to extract lung sounds. This structure utilizes a multilayer (hierarchical) approach to reduce the risk of converging to local minima and provides additional degrees of freedom to tune parameters (such as the number of layers and scaling factors) independently for each source type.
Periodicity-Based Selection: A key innovation is the exploitation of the periodic nature of heart and lung function without requiring prior knowledge of the specific period values. After the parallel modules generate candidate signals, the system estimates the period of each output using the autocorrelation function. The module output with the smaller period is selected as the heart sound, while the other is designated as the lung sound.

Key Contributions
The paper identifies three primary contributions:

Novel Algorithmic Structure: The introduction of a parallel, multilayer NMF architecture that allows for independent parameter tuning for heart and lung extraction, improving separation accuracy compared to single-module approaches.
Handling Mixed-Sign Signals: The adaptation of the affine NMF algorithm with a scale-and-offset block, enabling the method to process mixed-sign bioacoustic mixtures effectively.
Periodicity-Driven Separation: The utilization of the intrinsic periodicity of heart and lung sounds as a selection criterion for source identification. This approach improves accuracy without requiring manual segmentation or precise prior knowledge of signal periods, a feature not previously applied in NMF-based bioacoustic separation to the authors' knowledge.

Experimental Results
The method was evaluated on a synthesized dataset comprising 100 cases, where each case consisted of two mixtures of real-world heart and lung recordings. The performance was measured using Source-to-Distortion Ratio (SDR), Source-to-Interference Ratio (SIR), and Source-to-Artifacts Ratio (SAR).

Parameter Optimization: Through 100 experiments, optimal parameters were identified as $\alpha=0.5$ , with the heart detection block using 2 layers and the lung detection block using 1 layer.
Performance Metrics: The proposed method achieved an average SIR of 30.9 dB, an SAR of 17.1 dB, and an SDR of 21.2 dB.
Comparative Analysis: When compared to recent NMF-based methods (Tsai, Xie, Wang, and Candas), the proposed approach demonstrated superior performance, particularly in SIR, which the authors note is the most relevant metric for clinical purposes. The results showed significant improvements over existing methods, which often yielded lower SIR values (e.g., 10.4 dB to 24.1 dB in comparative studies).

Significance and Claims
The paper claims that the proposed method offers a superior solution for the blind source separation of heart and lung sounds by combining parallel processing, multilayer structures, and periodicity exploitation. The authors emphasize that the method achieves high accuracy without the need for manual intervention or extensive prior knowledge of the signal periods. While the results are based on synthesized mixtures of real measurements, the authors state that the method demonstrates "superior source separation accuracy" compared to other current methods. They conclude that the approach is promising for clinical application but note that further testing on actual clinical data is required in future studies. The paper maintains a modest tone regarding future implications, focusing strictly on the demonstrated improvements in separation metrics (SDR, SIR, SAR) over existing techniques.