Bayesian fusion of algorithms for the robust estimation of respiratory rate from the photoplethysmogram

Respiratory rate (RR) is a key vital sign that is monitored to assess the health of patients. With the increase of the availability of wearable devices, it is important that RR is extracted in a robust and noninvasive manner from the photoplethysmogram (PPG) acquired from pulse oximeters and similar devices. However, existing methods of noninvasive RR estimation suffer from a lack of robustness, resulting in the fact that they are not used in clinical practice. We propose a Bayesian approach to fusing the outputs of many RR estimation algorithms to improve the overall robustness of the resulting estimates. Our method estimates the accuracy of each algorithm and jointly infers the fused RR estimate in an unsupervised manner, with aim of producing a fused estimate that is more accurate than any of the algorithms taken individually. This approach is novel in the literature, where the latter has so far concentrated on attempting to produce single algorithms for RR estimation, without resulting in systems that have penetrated into clinical practice. A publicly-available dataset, Capnobase, was used to validate the performance of our proposed model. Our proposed methodology was compared to the best-performing individual algorithm from the literature, as well as to the results of using common fusing methodologies such as averaging, median, and maximum likelihood (ML). Our proposed methodology resulted in a mean-absolute-error (MAE) of 1.98 breaths per minute (bpm), outperformed other fusing strategies (mean fusion: 2.95 bpm; median fusion: 2.33 bpm; ML: 2.30 bpm). It also outperformed the best single algorithm (2.39 bpm) and the benchmark algorithm proposed for use with Capnobase (2.22 bpm). We conclude that the proposed fusion methodology can be used to combine RR estimates from multiple sources derived from the PPG, to infer a reliable and robust estimation of the respiratory rate in an unsupervised manner.