1. An X-ray CT apparatus comprising; an X-ray generator configured to generate X-rays; an X-ray detector configured to detect the X-rays after passing through a subject and obtain measured projection data; a rotating plate configured to mount the X-ray generator and the X-ray detector thereon, and rotate around the subject; a local measured projection data extractor configured to reconstruct a first CT image relating to a first reconstruction range of the subject, from the measured projection data obtained by the X-ray detector, and use the first CT image to extract from the measured projection data, local measured projection data in association with a second reconstruction range within the first reconstruction range; and a second iterative approximate reconstructor configured to reconstruct a second CT image relating to the second reconstruction range, from the local measured projection data, and performs iterative correction on the second CT image, so that local calculated projection data obtained by subjecting the second CT image to forward projection by calculation, becomes equal to the local measured projection data extracted by the local measured projection data extractor, wherein, the local measured projection data extractor comprising a first iterative approximate reconstructor configured to perform the iterative correction on the first CT image, so that calculated projection data obtained by subjecting the first CT image to the forward projection by calculation becomes equal to the measured projection data detected by the X-ray detector, and use the first CT image iteratively corrected so as to extract the local measured projection data in association with the second reconstruction range; and wherein, the local measured projection data extractor comprises a first weight selector configured to select a weight to be used for the iterative correction on the first CT image, and the second iterative approximate reconstructor comprises a second weight selector configured to select a weight to be used for the iterative correction on the second CT image, wherein, each of the first weight selector and the second weight selector selects either one of a statistical value weight and a constant value weight, the statistical value weight being various weight to be given to output data from plural detection elements constituting the X-ray detector, in response to magnitude of the output, and the constant value weight being an identical weight to be given to the output data from the plural detection elements.