Data-Driven Respiratory Signal Extraction for SPECT Imaging Using Laplacian Eigenmaps

In Single Photon Emission-Computed Tomography (SPECT) imaging, respiratory motion may lead to artifacts and loss of quantitative accuracy. To compensate for this motion, a respiratory surrogate signal representing the patient's respiratory state over time is required. In practice, this surrogate signal is obtained via sensor-based approaches, but we seek to develop a data-driven solution that requires no external hardware. In this work, we compare two such methods, one linear and one non-linear, based on dimensionality reduction: Principle Component Analysis (PCA) and Laplacian Eigenmaps (LE). Our aim is to apply both to conventional SPECT and assess the feasibility of data-driven respiratory surrogate signal extraction for this modality. We expect that LE, which is less sensitive to outliers in data, will outperform PCA at high levels of image noise. Two phantom acquisitions were performed: one in which a sphere in cold background was translated axially by a piston actuator (dynamic), and a warm background with no sphere (static). Using binomial subsampling, both datasets were combined at various Signal-to-Noise Ratios (SNRs). LE and PCA surrogate signals were computed and compared via Pearson's correlation to the truth signal obtained from the actuator. As a follow-up, LE and PCA estimates from 27 cardiac SPECT acquisitions were compared to a simultaneously acquired signal from a pressure sensor embedded in an elastic belt. In the phantom experiment, correlations between LE/ PCA and truth were > 0.9 for all SNR > 5. For SNR < 5, PCA deteriorated rapidly, whereas LE remained stable through SNR=2.5. For the patient validation, LE and PCA yielded average correlations of 0.86 +/- 0.14 and 0.37 +/- 0.26, respectively. The phantom experiment indicated that LE outperforms PCA for low-SNR data. This conclusion was supported by the superior performance of LE for patient datasets, where noise may be high. However, the present work is limited by the simplistic motion present in the phantom experiment and the limited scope of the patient validation.