Positron emission tomographs (PETs) are currently almost exclusively designed as hybrid systems. The current standard is the PET/CT combination, while prototype PET/MRI systems are being studied by several research groups. One problem in these systems is that the transaxial field-of-view of the second system is smaller than that of the PET camera and does not provide complete attenuation data. Because this second system provides the image for PET attenuation and scatter correction, the smaller FOV causes truncation of the attenuation map, producing bias in the attenuation corrected activity image. In this paper, we propose a maximum-a-posteriori algorithm for estimating the missing part of the attenuation map from the PET emission data. The method is evaluated on five artificially truncated $^{18}{\rm F \mathchar"702D FDG PET/CT}$ studies, where it reduced the error on the reconstructed PET activities from 20% to less than 7%. The results on a PET/MRI patient study with $^{18}{\rm F \mathchar"702D FDG}$ are presented as well.