Efficient time-weighted sensitivity image calculation for motion compensated list mode reconstruction

Accurate motion compensated image reconstruction of freely moving small animals requires the exact calculation of the time-weighted sensitivity correction factors. Back-projection of all possible lines of response for every recorded pose is a computationally intensive task, which requires impractically long reconstruction times. In this work we investigated an approach to accelerate this task, by randomly sampling the lines of response and the poses that are used to calculate the time-averaged sensitivity image. Two phantom datasets, acquired on the microPET Focus220 scanner, were used to quantify errors introduced in the randomly sampled sensitivity images and propagated to the final reconstructed images. In addition, the qualitative performance of the proposed methodology was assessed by reconstructing a freely moving rat acquisition. Results showed that randomisation can severely amplify the noise in the reconstructed images, especially when few LORs are sampled. However, such errors can be suppressed by post-filtering the randomised sensitivity images prior to reconstruction (e.g. 2 mm FHWM). Such an approach can substantially reduce the computational time involved during the estimation of the time-averaged sensitivity image for motion compensated image reconstruction.