Positron emitters are activated by proton beams in proton radiotherapy, and positron emission tomography (PET) images can thus be used for dose verification. Since a PET image is not directly proportional to the delivered radiation dose distribution, predicted PET images are compared to measured PET images and an agreement of both indicates a successful irradiation. Such predictions are given on the basis of Monte Carlo calculations or a filtering approach which uses a convolution of the planned dose with specific filter functions to estimate the PET activity. In this paper, we describe and evaluate a dose reconstruction method based on PET images which reverses the just mentioned convolution approach using appropriate deconvolution methods. Deconvolution is an ill-posed inverse problem, and suitable regularization techniques are required in order to guarantee a stable solution. The basic convolution approach is developed for homogeneous media and additional procedures are necessary to generalize the PET estimation to inhomogeneous media. This generalization formalism is used in our dose deconvolution approach as well. Various simulations demonstrate that the dose reconstruction method is able to reverse the PET estimation method both in homogeneous and inhomogeneous media. Measured PET images are however degraded by noise and artifacts and the dose reconstructions become more difficult and the results suffer from artifacts as well. Recently used in-room PET scanners allow a decreased delay time between irradiation and imaging, and thus the influence of short-lived positron emitters on the PET images increases considerably. We extended our dose reconstruction method to process PET images which contain several positron emitters and simulated results are shown.