Non-pure positron emitters, with their long half-lives, allow for the tracing of slow biochemical processes which cannot be adequately examined by the commonly used short-lived positron emitters. Most of these isotopes emit high-energy cascade gamma rays in addition to positron decay that can be detected and create a triple coincidence with annihilation photons. Triple coincidence is discarded in most scanners, however, the majority of the triple coincidence contains true photon pairs that can be recovered. In this study, we propose a strategy for recovering triple coincidence events to raise the sensitivity of PET imaging for non-pure positron emitters. To identify the true line of response (LOR) from a triple coincidence, a framework utilizing geometrical, energy and temporal information is proposed. The geometrical criterion is based on the assumption that the LOR with the largest radial offset among the three sub pairs of triple coincidences is least likely to be a true LOR. Then, a confidence time window is used to test the valid LOR among those within triple coincidence. Finally, a likelihood ratio discriminant rule based on the energy probability density distribution of cascade and annihilation gammas is established to identify the true LOR. An Inveon preclinical PET scanner was modeled with GATE (GEANT4 application for tomographic emission) Monte Carlo software. We evaluated the performance of the proposed method in terms of identification fraction, noise equivalent count rates (NECR), and image quality on various phantoms. With the inclusion of triple coincidence events using the proposed method, the NECR was found to increase from 11% to 26% and 19% to 29% for I-124 and Br-76, respectively, when 7.4-185 MBq of activity was used. Compared to the reconstructed images using double coincidence, this technique increased the SNR by 5.1-7.3% for I-124 and 9.3-10.3% for Br-76 within the activity range of 9.25-74 MBq, without compromising the spatial resolution or contrast. We conclude that the proposed method can improve the counting statistics of PET imaging for non-pure positron emitters and is ready to be implemented on current PET systems.