In order to provide an arithmetic device, an X-ray CT apparatus, and an image reconstruction method, capable of reducing processing time while maintaining a noise reduction effect, in a successive approximation image reconstruction method (separable paraboloidal surrogate (SPS) method) of the related art, updated images are forward-projected, whenever images are repeatedly updated, a difference between forward projection data and original object projection data is back-projected so that a difference image is obtained, and a forward projection process and a back projection process are repeatedly performed, but, in the present invention, a forward projection process and a back projection process requiring calculation time are replaced with a process requiring a relatively small calculation amount, such as a difference between an updated image and a reference image, and, as a result, it is possible to considerably reduce a calculation amount in a successive approximation image reconstruction process and to reduce processing time.
