  Objective: We aimed to fuse the outputs of different
electrocardiogram-derived respiration (EDR) algorithms to create one EDR signal
that is of higher quality. Methods: We viewed each EDR algorithm as a software
sensor that recorded breathing activity from a different vantage point,
identified high-quality software sensors based on the respiratory signal
quality index, aligned the highest-quality EDRs with a phase synchronization
technique based on the graph connection Laplacian, and finally fused those
aligned, high-quality EDRs. We refer to the output as the sync-ensembled EDR
signal. The proposed algorithm was evaluated on two large-scale databases of
whole-night polysomnograms. We evaluated the performance of the proposed
algorithm using three respiratory signals recorded from different hardware
sensors, and compared it with other existing EDR algorithms. A sensitivity
analysis was carried out for a total of five cases: fusion by taking the mean
of EDR signals, and the four cases of EDR signal alignment without and with
synchronization and without and with signal quality selection. Results: The
sync-ensembled EDR algorithm outperforms existing EDR algorithms when evaluated
by the synchronized correlation ({\gamma}-score), optimal transport (OT)
distance, and estimated average respiratory rate (EARR) score, all with
statistical significance. The sensitivity analysis shows that the signal
quality selection and EDR signal alignment are both critical for the
performance, both with statistical significance. Conclusion: The sync-ensembled
EDR provides robust respiratory information from electrocardiogram.
Significance: Phase synchronization is not only theoretically rigorous but also
practical to design a robust EDR.
