Sequential weighted least squares algorithm for PET image reconstruction

The weighted least squares (WLS) algorithm has proven useful for modern positron emission tomography (PET) scanners to approach reconstructions with non-Poisson precorrected measurement data. In this paper, we propose a new time recursive sequential WLS algorithm whose derivation uses the time-varying property of data acquisition of PET scanning. It ties close relationship with the time-varying Kalman filtering and can be extended appropriately to an iteration fashion as the absence of proper a priori initializations. The performance of sequential WLS is evaluated experimentally. The results show its fast convergence over both the multiplicative and coordinate-based iterative WLS methods. It also produces relative uniform estimate variances that makes it more suitable for routine applications.