1. An X-ray CT apparatus comprising: an X-ray generation part that generates X-rays, an X-ray detection part that detects X-rays that transmit through an imaging object, and obtains measured projection data, a rotation plate that carries the X-ray generation part and the X-ray detection part, and rotates around the imaging object, and a successive approximate reconstruction part that reconstructs a CT image from the measured projection data obtained by the X-ray detection part for a reconstruction area of the imaging object, obtains calculated projection data by performing forward projection of the CT image by calculation, and successively corrects the CT image so that the calculated projection data and the measured projection data become equal to each other, wherein the successive approximate reconstruction part comprises a noise measurement part that calculates noise intensity in the CT image for at least a predetermined region of interest, and successively corrects the CT image of the region of interest by using the noise intensity calculated by the noise measurement part.