1. An X-ray imaging apparatus comprising, an X-ray source configured to generate X-rays from an X-ray focus, an X-ray detector having a two-dimensional array of plural detector elements, configured to detect the X-rays emitted from the X-ray source and passing through a subject, a rotary mechanism configured to rotate the X-ray source and the X-ray detector which are opposed to each other, and an operation part configured to reconstruct a tomographic image of the subject, by using plural projection data items detected by the X-ray detector, according to emission of the X-rays from the X-ray source along with rotating an emitting direction of the X-rays, wherein, the plural projection data items include a first sinogram where acquired data items are arranged, with a first axis representing detector element numbers in a rotation direction of the X-ray detector, and a second axis representing projection numbers respectively associated with rotation angles of the X-ray source, and the operation part comprises a data interpolation part configured to interpolate the first sinogram, and an image reconstruction part configured to reconstruct an image by using a second sinogram that is generated by the data interpolation part, the data interpolation part performs interpolation along various angles θ, in making up for data deficiency included in the first sinogram or in rearranging the data items in the form suitable for a reconstruction process, so as to generate plural second sinograms, and the image reconstruction part performs an image reconstruction process including a process of weighted averaging of the plural second sinograms, using a weight corresponding to an angle difference between the angle θ and a slope of a trajectory on the second sinogram, depicted by a virtual point placed on a pixel position targeted for reconstruction.