1. An X-ray CT apparatus, comprising, an X-ray irradiation unit for irradiating X-rays, an X-ray detecting unit for detecting the X-rays that have passed through a subject and generating X-ray detecting data, a calculation unit of projection data for subjecting the X-ray detecting data to logarithmic conversion and generating projection data, a filter processing unit for smoothing at least one of the X-ray detecting data and the projection data, and an image calculation unit for calculating from the projection data acquired in the filter processing unit, a CT image which represents a distribution of X-ray attenuation coefficient, wherein, the filter processing unit generates boundary data by using at least a part of the X-ray detecting data and the projection data, and performs smoothing processing on at least one of the X-ray detecting data and the projection data, using the boundary data as a threshold.