Simultaneous Estimation of Temporal Basis Functions and Fully 4D PET Images

Fully 4D joint-estimation of temporal basis functions and dynamic positron emission tomography (PET) images was recently proposed by the authors. The method alternately estimates both a global set of temporal basis functions and the corresponding coefficient for each basis function for each image voxel. A fully 4D version of the Expectation Maximization (EM) algorithm is used with two different models of the mean of the Poisson measured data, each model allowing either the coefficients or the basis functions to be estimated. However, the current (alternating) method requires distinctly separate steps to estimate the two sets of unknowns. In this work the backprojected data within the EM algorithm are exploited to permit a simultaneous update of both the basis functions and the coefficients - hence reducing calculation time by almost a factor of two and also removing the need to specify the number of iterations performed for each step before switching between the estimation processes. The improvements in image quality obtained with the original fully 4D alternating method are retained with the simultaneous estimation method.