1. A medical imaging apparatus comprising: a data acquirer configured to acquire measured data acquired by detecting X-ray transmitted by an X-ray source to an object; and an image processor configured to: acquire an initial image based on the measured data; estimate a difference between data acquired by re-projecting an inside of a region of interest (ROI) in the initial image and the measured data as an ROI-outside measured data; acquire an ROI-outside image by back-projecting the ROI-outside measured data; estimate a difference between data acquired by re-projecting the ROI-outside image and the measured data as an ROI-inside measured data; and acquire a reconstructed image based on the ROI-inside measured data, wherein the image processor is further configured to alternately estimate the ROI-outside measured data and the ROI-inside measured data.