A method and apparatus is provided to correct for scatter in a positron emission tomography (PET) scanner, the scatter coming from both within and without a field of view (FOV) for true coincidences. For a region of interest (ROI), the outside-the-FOV scatter correction are based on attenuation maps and activity distributions estimated from short PET scans of extended regions adjacent to the ROI. Further, in a PET/CT scanner, these short PET scans can be accompanied by low-dose X-ray computed tomography (CT) scans in the extended regions. The use of short PET scans, rather than full PET scans, provides sufficient accuracy for outside-the-FOV scatter corrections with the advantages of a lower radiation dose (e.g., low-dose CT) and requiring less time. In the absence of low-dose CT scans, an atlas of attenuation maps or a joint-estimation method can be used to estimate the attenuation maps for the extended regions.