We describe an iterative reconstruction algorithm (HYPR-OSEM) which improves the signal-to-noise ratio (SNR) in single frame static imaging by incorporating the HighlY constrained back-PRojection (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 was updated every main iteration. 3 strategies were used to apply the HYPR operator in OSEM: i) within the image space modeling component of the system matrix for forward-projection only (HYPR-F-OSEM), ii) within the image space modeling component for both forward-projection and back-projection (HYPR-FB-OSEM), and iii) on the new image estimate after each OSEM subset update (HYPR-AU-OSEM). Resolution and contrast phantom simulations with various sizes of hot and cold regions were used to evaluate the performances of various forms of HYPR-OSEM with respect to OSEM and OSEM with a post reconstruction filter. Although the convergence in contrast recovery coefficients (CRC) obtained from all forms of HYPR-OSEM was observed to be slower than that from OSEM (with AU being the fastest among the 3 forms), HYPR-OSEM achieved up to 2-3 times lower noise level for a fixed CRC as compared to OSEM in the simulations conducted. When comparing to the filtered OSEM, HYPR-OSEM images contained similar noise level but with higher CRC due to the preservation of resolution in the HYPR-OSEM images. In summary, HYPR-OSEM can improve the SNR without degrading the resolution or contrast. In general, it can achieve: better accuracy in CRC at equivalent noise level than OSEM, better precision than OSEM, and better accuracy than filtered OSEM. In addition to static imaging, the proposed method can be applied to improve the image quality of any frame-based iterative reconstruction for both SPECT and PET.