Image quality deterioration due to a drop in resolution or lowering of S/N ratio while reducing the amount of data stored during a 3D data acquisition process, and shortening the time from the start of an examination to the end of imaging. The method and apparatus of this invention perform, in parallel with the 3D data acquisition process, addition of sinograms, reading of subsets of the sinograms having been added, and image reconstruction. Consequently, the amount of data stored is reduced, and the time from the start of an examination to the end of imaging is shortened. At the same time, since 3D iterative reconstruction is not accompanied by conversion from 3D data to 2D data, a drop in resolution due to errors occurring with the conversion from 3D data to 2D data is avoided. The 3D iterative reconstruction can directly incorporate processes such as an attenuation correction process. It is thus possible to avoid also a lowering of S/N ratio resulting from an indirect incorporation of such processes.