Positron emission tomography (PET) is one of the key molecular imaging modalities in medicine and biology. Penalized iterative image reconstruction algorithms frequently used in PET are based on maximum-likelihood (ML) and maximum a posterior (MAP) estimation techniques. The ML algorithm produces noisy artifacts whereas the MAP algorithm eliminates noisy artifacts by utilizing availableprior information in the reconstruction process. The MAP-based algorithms fail to determine the density class in the reconstructed image and hence penalize the pixels irrespective of the density class and irrespective of the strength of interaction between the nearest neighbors. A Hebbian neural learning scheme is proposed to model the nature of interpixel interaction to reconstruct artifact-free edge preserving reconstruction. A key motivation of the proposed approach is to avoid oversmoothing across edges that is often the case with MAP algorithms. It is assumed that local correlation plays a significant role in PET image reconstruction, and proper modeling of correlation weight (which defines the strength of interpixel interaction) is essential to generate artifact-free reconstruction. The Hebbian learning-based approach modifies the interaction weight by adding a small correction that is proportional to the product of the input signal (neighborhood pixels) and output signal. Quantitative analysis shows that the Hebbian learning-based adaptive weight adjustment approach is capable of producing better reconstructed images compared with those reconstructed by conventional ML and MAP-based algorithms in PET image reconstruction.