1. A tomographic image generating apparatus comprising: a radiation source for applying radiation to a subject; a radiation detector for detecting radiation that has passed through the subject and acquiring projection image data from the detected radiation; and a tomographic image generating unit for generating a tomographic image in a region of interest disposed in the subject and interposed between the radiation source and the radiation detector, using a plurality of projection image data acquired by the radiation detector in image capturing processes, which are carried out while a relative positional relationship between the radiation source and the radiation detector successively changes, wherein the tomographic image generating unit includes a data determiner for performing an extrapolating process on each of the acquired projection image data along a prescribed direction, and for performing a smoothing process on each of the acquired projection image data along a direction perpendicular to the prescribed direction, thereby determining values of a plurality of pixels in non-detecting regions, which do not belong to a detecting region of the radiation detector, the determined values of the pixels also being used to generate the tomographic image.