Theoretical comparison of uniform resolution penalized likelihood dynamic PET images with multiframe penalized likelihood static PET images

We validate our theoretical approximations for the mean and variance properties of instantaneous activity estimates obtained via penalized likelihood (PML) dynamic PET reconstructions. We then use these approximations together with their previously derived and validated counterparts for static PET to compare the bias/variance (equivalently resolution/noise) tradeoffs involved in both dynamic and static reconstructions from simulated data. For the dynamic case, the degree of spatial and temporal smoothing is controlled by the spatial and temporal smoothing parameters. For the static case, spatial smoothing is controlled by the spatial smoothing parameter while the degree of temporal smoothing is determined by the number of temporal frames and the amount of interframe overlap. By varying these parameters we were able to compute approximate bias and variances for activity estimates over a large range of spatial and temporal smoothing levels. Theoretical approximations showed that dynamic reconstructions result in lower variance at matched bias levels and vice versa. We also show how spatial resolution can be kept uniform over space and time by applying spatiotemporally varying smoothing and also performing the reconstruction in a transformed time domain. The combination of these results indicate that our penalized ML dynamic PET reconstruction algorithm is capable of outperforming multiframe static reconstructions interms of the bias/variance tradeoff while preserving resolution uniformity in space and time