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 region of interest of the CT image by using the noise intensity calculated by the noise measurement part, wherein the noise measurement part includes: a division calculation part that divides the measured projection data into M sets of measured projection data, a divided image calculation part that reconstructs a CT image for each of the M sets of the measured projection data divided by the division calculation part, and a divided noise measurement part that obtains a difference image of the M sets of the CT images reconstructed by the divided image calculation part, and calculates a variation of the CT values of the region of interest in the difference image as the noise intensity, wherein the X-ray detection part contains a plurality of X-ray detection elements disposed along a channel direction and a slice direction, and the X-ray detection part detects the X-rays at a plurality of projection angles while the rotation plate rotates one time, wherein the division calculation part divides the measured projection data for at least two directions among the channel direction, the slice direction, and a projection angle direction, and wherein the noise measurement part chooses at least two directions for the division of the measured projection data performed by the division calculation part from the channel direction, the slice direction, and the projection angle direction, uses a sum of noise intensities obtained and weighted for the respective directions as the noise intensity, and changes weights according to the position of the region of interest in the CT image.