Robust Divergences and Cost Functions in Non-negative Matrix Factorization for Heart-Rate Estimation from Audio Signals

Microphone-based heart rate (HR) monitoring is increasingly being explored as a non-contact method for healthcare, especially in home and hospital environments. A common issue is that audio recordings in these contexts are prone to background interference, abrupt transient noise, and device variability. To overcome this challenge, we propose a non-negative matrix factorization (NMF)-based Huber loss cost function optimization. The input audio signal is first converted into a magnitude spectrogram using Short-Time Fourier Transform (STFT), then the Singular Value Decomposition (SVD) parameterization method is used to reduce its dimensions to retain the dominant spectral energy. A robust Non-Negative Matrix Factorization (NMT) algorithm is then applied to decompose the spectrogram into its spectral bases and temporal activations via projected gradient descent to enhance robustness against outliers and non-Gaussian noise. To identify heart-related components, each temporal basis is evaluated using its spectral centroid, and those within the 0-300 Hz range, which is the range for heart-related activities, are selected, and Wiener filtering is used to reconstruct a clear version of the signal. The selected temporal activation patterns are then analyzed in the frequency domain to detect the dominant frequency associated with the heartbeat. The final heart rate was estimated by identifying the dominant frequency band within 1 Hz to 2 Hz and converting it to beats per minute (BPM). To evaluate the performance of the developed method, Gaussian noise was added at signal-to-noise ratios ranging from 5 to 20 dB, and the experimental result was evaluated using mean absolute error (MAE), root mean squared error (RMSE), average absolute error percentage (AAEP), and relative root index (RRI).