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The authors consider detection of high-energy photons in positron emission tomography using thick scintillation crystals. Parallax effect and multiple Compton interactions in such crystals significantly reduce the accuracy of conventional detection methods. In order to estimate the photon line of flight based on photomultiplier responses, the authors use asymptotically optimal nonlinear techniques, implemented by feedforward and radial basis function neural networks. Incorporation of information about angles of incidence of photons significantly improves accuracy of estimation. The proposed estimators are fast enough to perform detection, using conventional computers. Monte Carlo simulation results show that their approach significantly outperforms the conventional Anger algorithm.