Despite its success in many biomedical applications, Positron Emission Tomography (PET) has the drawback of typically having lower spatial resolution and higher noise respect to other medical imaging techniques. The best achievable spatial resolution in PET scanners is limited by factors such as the positron range, non-collinearity and the size of the detector crystals. In this work, we present a novel method that uses series of image reconstructions (super-iterations) to go beyond the expected resolution-noise limits for a given PET acquisition. The image quality improvement is achieved using the projections of the previous image reconstruction to redistribute the measured counts of each line-of-response (LOR) into several subLORs, from which a new activity distribution with better quality is reconstructed. The method was evaluated with data from the preclinical scanner 4R-SuperArgus PET/CT, using the NEMA NU4-2008 image quality phantom, a cold Derenzo phantom, and an in-vivo FDG cardiac study on a rat. Resolution and recovery coefficient (RC) improvement of ~10% was achieved while keeping the same noise level. Qualitative results from the in-vivo study also confirm this improvement in image quality. The proposed method is able to achieve significantly better images at the expense of a modest increase of the computational time, and it could be also applied to other modalities, such as SPECT and Compton Cameras.