PET-MR respiratory signal estimation using semi-supervised manifold alignment

In simultaneous PET-MR scanning, respiratory motion can lead to artefacts and blurring in both PET and MR images, negatively impacting research and clinical applications. This can be compensated for by estimating respiratory motion through a respiratory signal. Here, we propose a data-driven dimensionality-reduction-based technique which aligns manifolds formed from both PET and MR data to produce a robust signal even in situations where MR data are unavailable, as expected in realistic workflows. To handle the missing MR data, 3 methods for semi-supervised manifold alignment alignment were tested using a semi-synthetic dataset consisting of 500 0.64 s dynamic MR volumes and PET sinograms. It was found that implicit correspondences for unlabelled PET data were most effective on average for signal estimation, at 81 ± 4% mean correlation to a gold standard diaphragmatic navigator, compared to 89 ± 0.2% when using MR only with no missing data. Two explicit correspondence estimators, based on graph theory, performed poorly, with 1-to-1 and many-to-1 correspondences achieving 34 ±16% correlation and 31 ± 9% correlation, respectively.