Reconstruction in positron emission tomography is performed with partially known attenuation. A PET-CT scanner is used to generate a PET image with time of flight emission information. To limit x-ray dose while providing increased sensitivity at the ends of the CT volume in the PET image, attenuation coefficients for oblique LORs passing outside the CT volume are determined from the time of flight emission information. The attenuation coefficients for LORs within the CT volume are derived from the CT data. An objective function may be maximized for the emission distribution without reconstructing the attenuation distribution.
