1. An X-ray CT apparatus, comprising: an X-ray source configured to generate X-rays while rotating along a circuital orbit around a subject; an X-ray detector having a plurality of channels and configured to detect the X-rays transmitted through the subject in each channel; a reconstruction function setting part configured to set the reconstruction function by weighting a predetermined reference reconstruction function based on statistics representing a statistical dispersion of an X-ray amount of the detected X-rays; and a reconstruction processor configured to carry out reconstruction of projection data generated from the detected X-rays, based on the reconstruction function to produce image data.