HighlY constrained back-PRojection (HYPR) is a post-processing de-noising technique originally developed for time-resolved magnetic resonance imaging. It has been recently applied to dynamic imaging for positron emission tomography and shown promising results. In this work, we have developed an iterative reconstruction algorithm (HYPR-OSEM) which improves the signal-to-noise ratio (SNR) in static imaging (i.e. single frame reconstruction) by incorporating HYPR de-noising directly within the ordered subsets expectation maximization (OSEM) algorithm. The proposed HYPR operator in this work operates on the target image(s) from each subset of OSEM and uses the sum of the preceding subset images as the composite which is updated every iteration. Three strategies were used to apply the HYPR operator in OSEM: (i) within the image space modeling component of the system matrix in forward-projection only, (ii) within the image space modeling component in both forward-projection and back-projection, and (iii) on the image estimate after the OSEM update for each subset thus generating three forms: (i) HYPR-F-OSEM, (ii) HYPR-FB-OSEM, and (iii) HYPR-AU-OSEM. Resolution and contrast phantom simulations with various sizes of hot and cold regions as well as experimental phantom and patient data were used to evaluate the performance of the three forms of HYPR-OSEM, and the results were compared to OSEM with and without a post reconstruction filter. It was observed that the convergence in contrast recovery coefficients (CRC) obtained from all forms of HYPR-OSEM was slower than that obtained from OSEM. Nevertheless, HYPR-OSEM improved SNR without degrading accuracy in terms of resolution and contrast. It achieved better accuracy in CRC at equivalent noise level and better precision than OSEM and better accuracy than filtered OSEM in general. In addition, HYPR-AU-OSEM has been determined to be the more effective form of HYPR-OSEM in terms of accuracy and precision based on the studies conducted in this work.