Fully 4D list-mode reconstruction with temporal basis function estimation

A fully 4D image reconstruction algorithm for emission tomography is proposed, which regards the temporal sequence of 3D images as a single 4D image composed of 4D basis functions. Each 4D basis function is factorised into a 3D spatial basis function and a 1D temporal basis function. The reconstruction algorithm estimates both a set of temporal basis functions as well as the corresponding set of weights for each of these functions for each spatial position in the field of view. The method is designed and evaluated within the framework of a direct 4D reconstruction of time-dependent list-mode positron emission tomography (PET) data. The advantages of the proposed method include: a) a notable reduction in the number of parameters to be estimated in the reconstruction, and b) every single image in the time series can potentially benefit from the acquired data over all points in time (depending on the temporal extent of the estimated time-basis functions). Evaluation of the method with simulated 4D Monte Carlo list-mode data indicates that this method has markedly lower spatial and temporal noise compared to the conventional independent time-frame reconstruction approach.