A late fusion multi-task learning for respiratory waveform and rate estimation from photoplethysmography

Continuous respiratory monitoring enables early detection of physiological deterioration, yet conventional capnography remains impractical for prolonged use. Photoplethysmography (PPG) offers a non-invasive alternative that encodes respiratory information through baseline wander (respiratory-induced intensity variation; RIIV), amplitude modulation (respiratory-induced amplitude variation; RIAV), and frequency modulation (respiratory-induced frequency variation; RIFV) of the pulsatile waveform. Existing PPG-based deep learning approaches, whether operating on the raw signal or on these physiological modulations, are limited to single-task architectures that estimate either respiratory rate or reconstruct the respiratory waveform in isolation, without jointly addressing both outputs. We propose a late fusion multi-task framework in which dedicated encoder branches independently process each modulation before fusion, and dual decoders simultaneously reconstruct the respiratory waveform and estimate the respiratory rate. The framework was evaluated on the CapnoBase (n = 42) and BIDMC (n = 52) benchmarks across multiple training strategies. For respiratory-rate estimation, the best transfer-learning configurations achieved a mean absolute error (MAE) of 2.27 bpm on CapnoBase and 1.33 bpm on BIDMC. For waveform reconstruction, the corresponding MAE values were 19.00% and 20.90%, with moderate correlations (r = 0.662 and r = 0.591, respectively). Sequential transfer learning consistently outperformed all other strategies, whereas pooled training degraded both outputs, demonstrating that capnography-derived and impedance-derived waveforms are not interchangeable training targets. These findings establish that short-window PPG can simultaneously support respiratory-rate estimation and waveform reconstruction, when reference signal compatibility is explicitly addressed in multi-task training.