1. An image reconstructing apparatus comprising: a Gaussian-based expansion-data group creating unit that creates a group of Gaussian-based expansion data that is expanded from each of a group of projection data through linear combination based on a plurality of Gaussian functions having different center points; and a reconstruction-image creating unit that creates a reconstruction image by performing one of two sequences of processing sequentially on each of the group of the Gaussian-based expansion data created by the Gaussian-based expansion-data group creating unit, the two sequences of processing including a sequence of Fourier transform processing, one-dimensional inverse-Fourier transform processing, and back projection processing, and a sequence of Fourier transform processing and two-dimensional inverse-Fourier transform processing.