1. An X-ray CT apparatus comprising: an X-ray generating part configured to generate X-rays while rotating along a circuital orbit around the 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 the statistical dispersion of the X-ray amount of the detected X-rays; and a reconstruction processor configured to carry out reconstructing the projection data based on the detected X-rays based on the reconstruction function and produce image data.