A simple analytical model is developed that allows efficient absolute dose reconstruction in patients undergoing radiation treatments using proton beams. The model is based on the solution of the inverse problem of dose recovery from the 3D information contained in the PET signal, obtained immediately after the treatment. The core of the proposed model lies in the analytical calculation of the introduced positron emitters' species matrix (PESM) or kernel, facilitated by previously developed theoretical calculations of the proton energy fluence distribution. Once the PESM is known, the absolute dose distribution in a patient can be found from the deconvolution of the 3D activity distribution obtained from the PET scanner with the calculated species matrix. As an example, we have used FLUKA Monte Carlo code to simulate the delivery of the radiation dose to a tissue phantom irradiated by a parallel-opposed beam arrangement and calculated the resultant total activity. Deconvolution of the calculated activity with the PESM leads to the reconstructed dose being within 2% of that delivered.