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The boundary information derived from anatomical images can be incorporated into maximum a posteriori (MAP) reconstruction algorithms to improve the quality of reconstructed images in positron emission tomography (PET). However, challenges arise from mismatches between anatomical (CT) and functional (PET) images which are unavoidable in practice. The aim of this study is to devise a new approach to incorporating anatomical knowledge into emission tomographic reconstruction which is robust to the mismatches while still improving the quality of reconstructed PET images. An anatomically based regionally adaptive regularization MAP (RMAP) is presented. The anatomical knowledge is introduced by labeling the current estimate of the PET image with different anatomical regions derived from the corresponding CT image. An intensity selective non-convex prior is used to model the local smoothness properties adaptively in each anatomical region. The regionally adaptive priors are then combined to form a prior in the Bayesian formulation for the next iteration in the reconstruction. Simulated results show that the proposed algorithm yielded superior lesion contrast recovery, bias- variance tradeoff and robustness to the mismatches between anatomical and functional images compared with MAP with a conventional non-convex prior and MAP with anatomical prior.