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 uniformly distributed at positional coordinates; 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, wherein the reconstruction-image creating unit executes Fourier transform on each of the group of the Gaussian-based expansion-data by calculating a simple sum of product directly using a corresponding expansion coefficient that is calculated when expanding each of the group of projection data by a corresponding one of the Gaussian functions and thereby statistical noises are removed from the projection data while high-frequency components corresponding to profile information about internal structures are left substantially intact without executing a low-pass filter processing.