A method of minimizing a patient's exposure to CT scan radiation during the mu-map generation process in a long axial field of view (FOV) PET scan includes performing a long axial FOV PET scan on a patient; performing one or multiple truncated FOV CT scan of a region in the patient's body in which the organs of interest lies; generating a truncated mu-map covering the truncated CT FOV; and generating a mu-map for the whole long axial FOV of the PET scan by extending the truncated mu-map generated from the truncated FOV CT scan by estimating the missing mu-map data using the PET data.