The non-negativity constraint inherently present in OSEM reconstruction successfully reduces the standard deviation in cold regions but at the cost of introducing a positive bias, especially at low iteration numbers. For low-count data, as often encountered in short-duration frames in dynamic imaging protocols, it has been shown that it can be advantageous (in terms of bias in the reconstructed image) to remove the non-negativity constraint. In this work two competing algorithms that do not impose non-negativity in the reconstructed image are investigated: NEG-ML and AB-OSEM. It was found that the AB-OSEM reconstruction outperformed the NEG-ML reconstruction. The AB-OSEM algorithm was then further developed to allow a forward model that includes randoms and scatter background terms. In addition to static reconstruction the current analysis was extended to consider the important case of kinetic parameter estimation from dynamic PET data. Simulation studies (comparing OSEM, FBP and AB-OSEM) showed that the positive bias obtained with OSEM reconstruction can be avoided in both static and parametric imaging through use of a negative lower bound in AB-OSEM reconstruction (i.e. by lifting the implicit non-negativity constraint of OSEM). When quantification tasks are considered, the overall error in the estimates (composed of both bias and standard deviation) is often of primary concern. An important finding of this work is that in most cases the activity concentration and the kinetic parameters obtained from images reconstructed using AB-OSEM showed a lower overall root mean squared error compared to the popular choices of either OSEM or FBP reconstruction for both cold and warm regions. As such, AB-OSEM should be preferred instead of the standard OSEM and FBP reconstructions when kinetic parameter estimation is considered. Finally, this work shows example parametric images from the high-resolution research tomograph obtained using the different reconstruction methods.