1. A radiography system comprising: a radiation source mounted movable to multiple positions of different projection angles relative to an imaging subject which is placed at a predetermined position; a radiographic image detector which detects a radiographic image of the subject by detecting radioactive rays that have penetrated the subject; an imaging controller which controls the radiation source to move within a range of a designated sweep angle and project radioactive rays toward the subject at different projection angles, while controlling the radiographic image detector to detect a set of radiographic images each at a different projection angle; a reconstruction processor which reconstructs the set of radiographic images of the subject acquired at multiple projection angles so as to produce a plurality of tomographic images of the subject, which are used for diagnosis; a process sequence controller which determines a parameter for sorting the plurality of tomographic images into a first group and a second group according to the sweep angle and controls the reconstruction processor on the basis of the parameter so as to produce the first group of tomographic images prior to the second group of tomographic images; and a display device which displays at least the first group of tomographic images for determination on whether the tomographic images are adequate for use in diagnosis.