The LM-EM algorithm has the advantage to calculate the emission probabilities needed for the reconstruction process on the fly, without the need of a pre-calculated system matrix. The reconstruction time for this algorithm strongly depends on the used backprojector and the available statistics. This algorithm when implemented in systems using monolithic crystals to detect gamma radiation allows one to extensively exploit the virtual pixilation feature, not available for systems based on pixilated crystals. In this work we present a backprojector for LM-EM, the TOR method, which achieves a tradeoff between computational efficiency and image quality. Its temporal subset algorithm optimization (LM-OS) has also been implemented in order to achieve real-time reconstructions. To evaluate the performances of LM-OS algorithm with the TOR method backprojector and only with one iteration on the datasets, studies based on the system spatial resolution, uniformity, and contrast coefficients were carried out and they were compared with those obtained with LM-EM and MLEM algorithms using twelve iteration. Finally, a study on reconstruction time using LM-OS has been performed with breast patients data.